Daf Yomi - Beitza 2 - Hachana by Reb Jay

According to Rabbah, things that were prepared on Yom Tov for Shabbos, or vice versa are assur m'Doraysa (Hachana D'Rabbah). Tosfos, the Rosh and the Ran learn this as the halacha. The Rambam holds that it is an issur D'rabanan. According to the Rishonim that learn Hachana D'Rabbah is an Issur D'oraysa, then how do we have an Eiruv Tavshilin? Tosfos asks this question and replies that the koach of an Eiruv Tavshilin is based on Ho'eel miklayea leahorchim (like Rav Chisda says; see Pesachim 46a). A nafka minah l'halacha would be, if it is muttar to cook before shkiah if the food will only be ready right before shkiah, thus not allowing for the theory that the cooking might be done for guests. The Rambam would hold it is muttar because of Eiruv Tavshilin, while Tosfos, the Rosh and the Ran would say that it is assur to cook at this time, as hachana is an issur D'oraysa, and there is no opportunity for ho'eel (in fact, the Magen Avraham writes that one who has made an Eiruv Tavshilin should not cook on Yom Tov for Shabbos late in the day for this reason--i.e, that it is k'die to be choshesh for the Rishonim that hold it is an issur D'oraysa--and therefore, one should endeavor to make early Shabbos when
Yom Tov leads into Shabbos).

Tosfos also writes that there is no stirah between Hachana D'Rabbah and an Eiruv Tavshilin , as Hachana D'Rabbah refers to something prepared by shamayim (like an egg) and not cooking or baking which involves already existing materials.