Introduction to Tractate Yevamos
It is written [Devarim 25: 5 – 10]: "If brothers dwell together, and one of them dies, and has no child, the wife of the dead shall not be married abroad to one not of his kin; her husbands' brother shall go into her, and take her to him to wife, and perform the duty of a husband's brother to her. And it shall be, that the firstborn that she bears shall succeed in the name of his brother that is dead, that his name be not blotted out of Israel. And if the man does not want to marry his brother's wife, then his brother's wife shall go up to the gate to the elders, and say: 'My husband's brother refuses to raise up to his brother a name in Israel; he will not perform the duty of a husband's brother to me.' Then the elders of his city shall call him, and speak to him; and if he stands, and says: 'I do not want to marry her'; then shall his brother's wife go up to him in the presence of the elders, and loose his shoe from off his foot, and spit before him; and she shall answer and say, 'So shall it be done to the man that does not build up his brother's house.' And his name shall be called in Israel, 'The house of him that had his shoe loosened'" (Deut. 25:5-10).
Rav Pinchas Kahati has an introduction to this tractate and to the details regarding the mitzvah of yibum. I present it to you in full. Here is the address where one can find the archives of any Mishna http://www.moreshet.net//oldsite/mishna/index.htm.
(1) The mitzvah of yibum applies only to brothers by the same father, and not to brothers by only the same mother, for it is written, "When brothers dwell with one another" – i.e., brothers who inherit with one another, thus excluding brothers who have only the same mother (Yev. 17b). Another opinion in the Gemara (ibid.) learns this law by tradition from the analogous use (gezerah shavah) of the word "brothers" referring to the sons of Jacob ("We are twelve brothers, sons of our father" – Gen. 42:32): just as the passage in Genesis refers to brothers by a common father and not by one mother, this passage also refers to brothers by the same father but not to brothers by the same mother. According to the Jerusalem Talmud, this law is implicit in the word "together" – "those who dwell in one house, excluding brothers by one mother (but different fathers), of whom one goes to the house of his father, and another goes to the house of his father."
(2) The phrase "and has no child [ben, lit., "son"] means, "and has no seed [zera]"; if, however, he does have descendants, even a daughter or a grandchild, the law of yibum does not apply to his widow.
(3) If the brother died without seed and left more than one wife (for formerly a Jew was permitted to be married simultaneously to several wives), one of his brothers marries by yibum, or submits to halitzah from, one of the wives, and thereby exempts all the rest from either yibum or halitzah, as it is written, "So shall it be done to the man that does not build up his brother's house," which it was understood to mean, he builds up one house but he does not build up two houses.
(4) Once a wife is exempt from the mitzvah of yibum, she becomes forbidden to marry her brother-in law under the prohibition of 'the brother's wife', of which it is written, "You shall not uncover the nakedness of your brother's wife" (Lev. 18:16). A baraita teaches: " 'The nakedness of your brother's wife' and 'her husband's brother shall go in to her' were stated in a single commandment" (Jer. Talmud, Ned. 3:2; Mekhilta; Sifri), i.e., the mitzvah of yibum alone exempts the yevamah from the prohibition of marrying the brother's wife, but the prohibition of the brother's wife applies to any woman who was released from the mitzvah of yibum.
(5) If the yevamah is prohibited to the yavam because of ervah (lit. "nakedness," i.e., family relationship), e.g., she is his daughter who had married his brother who died, or she is his wife's sister, then she is exempt from yibum. This is because it is written, "And you shall not take a woman to her sister, to be a rival to her, to uncover her nakedness beside the other" [aleha] (Lev. 18:18), and in the passage regarding yibum it is written, "her husband's brother shall go in to her [aleha]" – just as the latter is a case of mitzvah, so too is the former. Therefore the Torah stated, "And you shall not marry", i.e., even in order to perform the mitzvah of yibum it is prohibited to marry a woman and her sister; that yibum is prohibited in the other prohibited degrees of relationship is derived from the case of the wife's sister (Yev. 3b; 13a).
(6) Any woman who is exempted by Torah law from yibum is also exempt from halitzah, as it is written, "And if the man does not want to marry his brother's wife, then his brother's wife shall go up to the gate… and say : 'My husband's brother refuses to raise up to his brother a name in Israel…' and loose his shoe" (Deut. 25:7-9), from which it was understood that to whomever yibum applies, halitzah applies, and to whomever yibum does not apply, halitzah does not apply.
(7) If a man's brother died childless and left more than one wife, and one of them is prohibited to the yavam because of ervah, then just as the related woman is exempt from yibum and from halitzah, as was explained above, all the other wives of the dead man, who are called "her rivals" (see I Sam. 1:6), are similarly exempt from yibum and from halitzah, as it is written, "that does not build up his brother's house" – if he can build up the house in its entirety then he may build up part of a house, but he may not build up even part of a house which he cannot build up in it entirety.
(8) A widow who is prohibited due to ervah exempts not only her rivals from yibum and from halitzah, but also her rivals' rivals, and so on: e.g., Reuven died childless and left two wives, Leah and Hannah, and he had two brothers, Shimon and Levi, and Leah is the sister of Shimon's wife [Rahel]; in this case both yevamot, Leah and Hannah, are prohibited to Shimon: Leah, because she constitutes ervah for him, and Hannah, because she is the rival of a woman prohibited by ervah, as was explained above. Both of them are dependent upon Levi, however, for they are not related to him, and he must either marry by yibum or submit to halitzah from whicever one of them he wishes (Chart 1). If Levi married as his yevamah Hannah, i.e., the rival of the woman prohibited to his brother Shimon by ervah, and he (Levi) had another wife [Yehudit], and Levi also died childless, and his wives came before Shimon for yibum or halitzah – since Hannah is prohibited to him because of the ervah of her rival, then she also exempts her rival, i.e., Levi's second wife [Yehudit], from yibum and from halitzah. It follows from this that Leah, who is a woman prohibited to Shimon by ervah (since she is his wife's sister), exempts her rival and her rival's rival (Chart 2). This is also the law regarding her rival's rival's rival, ad infinitum. One view in the Gemara learns this from the passage, "And you shall not take a woman to her sister, to be a rival [li-tzror]" – since "li-tzror," and not "la-tzor" is written the Torah includes many rivals, i.e., the rival of the woman prohibited due to ervah, her rival's rival, her rival's rival's rival, and so on, all are exempt from yibum and from halitzah. Other authorities in the Gemara learn this law from other verses (see Yev. 8a). Rambam explains the reason for this law: in any case in which he has no zikah (the tie between a woman requiring yibum and the yavam) with her, she is prohibited to him forever on account of being his brother's wife; it follows from this that the rival of the woman prohibited by ervah is prohibited to him on account of ervah, and therefore she also exempts her rival (Hil. yibum 6:14-15); see also Rav Ashi's reason in the Gemara, Yev. 13a).
The Mishna states: Fifteen women exempt their co-wives and the co-wives of their co-wives from chalitzah (a ceremony by which the brother of the deceased man excuses himself from performing levirate marriage on the widow, which permits her to marry someone other than a brother of the deceased) and from yibum, until the end of the world. And these are the women: 1) his daughter, 2) and his daughter's daughter, 3) and his son's daughter, 4) his wife's daughter, 5) and her son's daughter, 6) and her daughter's daughter, 7) his mother-in-law, 8) and his mother-in-law's mother, 9) and his father-in-law's mother, 10) his maternal sister, 11) his mother's sister, 12) and his wife's sister, 13) his maternal brother’s wife, 14) the wife of his brother who was not in his world (this brother and the yavam were not alive at the same time), 15) and his daughter-in-law.
These women exempt their co-wives and the co-wives of their co-wives from chalitzah and from yibum, until the end of the world.
However, regarding all these women, if they died, or if they refused (a woman's annulment of a Rabinical marriage contracted for her in her minority), or if they were divorced, or if they were found to be an aylonis (an adult woman who did not develop any signs of female puberty and is incapable of bearing children), their co-wives are permitted. But you cannot say of his mother-in-law or his mother-in-law's mother or his father-in-law's mother that they were found to be an aylonis (since an aylonis cannot bear children) or that they refused (since only a minor can refuse).
How do they exempt their wives and co-wives? If his daughter or one of any of these arayos (a woman who it is prohibited to have relations with) was married to his brother, who had another wife, and he died childless, just as his daughter is exempt, so is her co-wife exempt.
If the co-wife of his daughter went and married to the second brother, who had another wife, and he died childless, just as his daughter's co-wife is exempt, so is her co wife’s co wife exempt, even if they are a hundred.
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[Reuven, Shimon and Levi are brothers. Reuven has a daughter Penina, born out of wedlock. Shimon marries Penina. He has also married a non-related woman, named Chana. Shimon dies childless and his wives fall for yibum to Reuven and Levi. Reuven cannot perform yibum with Penina since she is his daughter. Chana, the co-wife is also exempt. Levi performs a yibum with Chana. Levi has another wife, named Malka. Levi dies childless and his wives fall for yibum to Reuven. The Mishna teaches us that Reuven cannot perform a yibum with Malka since she is the co-wife’s (Chana) co wife.]
How is it that if they died or if they refused, or if they were divorced, or if they were found to be an aylonis, their co-wives are permitted? If his daughter or any other one of these arayos was married to his brother, who had another wife, and his daughter died, or was divorced, and afterwards his brother died childless, her co-wife is permitted.
And whoever could have refused but did not refuse, her co-wifel performs chalitzah but may not marry him by yibum. (2a – 2b)