(Mishnah): When Yom Tov occurs on a Friday, a person may not begin cooking a Shabbos meal on Yom Tov, but he may cook for Yom Tov and he can use the leftovers for Shabbos.

He can make a dish on Erev Yom Tov and rely on it (Eruv Tavshilin) to be able to cook on Yom Tov for Shabbos.

Beis Shamai say that he must prepare two dishes before Yom Tov. Beis Hillel require only one dish. But Beis Shamai agree that a fish with an egg cooked on it is considered to be two dishes.

If it was eaten or lost, he may not rely on it as the beginning of his Shabbos meal (to then be able to continue to cook on Yom Tov).

If any of the food remained, he may rely on it for Shabbos.

(Gemara): The Pasuk states (Shemos 16, 23), "bake what you want to bake (today); and cook what you want to cook (today)''. R. Eliezer says - one may bake when adding to that which was baked and one may cook when adding to that which was cooked. R. Yehoshua says - one may bake and cook when adding to that which was cooked.

What is the reasoning of R. Eliezer? As the Pasuk says, "bake what you want to bake (today); and cook what you want to cook (today)'' - the Pasuk separates them.

What is the reasoning of R. Yehoshua? He reads the Pasuk as, "...what you want to bake and what you want to cook, you should cook'' - the word 'and' teaches that 'you should cook' also refers back to 'what you want to bake'.

R. Eliezer (Amora): R. Eliezer (Tanna) follows the view that the Mitzvah of Shabbos was given to the Bnei Yisrael in Marah. Therefore, since the laws of Shabbos were already known, our Pasuk is superfluous and must be teaching about Eruv Tavshilin; but according to the view that it was given in Alush, they stood in Alush and were given this warning in Alush (as a law of Shabbos, that one may not cook on Shabbos, but it is not referring to Eruv Tavshilin).

Question: If it is a Torah prohibition to cook on Yom Tov (for afterwards), how could Eruv Tavshilin permit it?

Answer (R. Abahu): Strictly speaking, it is permitted to bake and cook on Yom Tov for Shabbos. However, Chazal prohibited it, to prevent a person coming to bake and cook for a weekday.

Proof: One may make the beds on Yom Tov for Shabbos (and Chazal were not concerned that one might prepare them for a weekday); so too one may bake and cook on Yom Tov for Shabbos.

R. Ila: Why is it permitted to make the beds on Yom Tov for Shabbos? Because one may make the beds on Shabbos night for Shabbos day (so people will not come to disrespect Yom Tov when they see him making beds).

Chazal do not permit baking and cooking on Yom Tov for Shabbos as one cannot bake or cook on Shabbos night for Shabbos day!

R. Kahana son of R. Chiya bar Ba: Cooking for Yom Tov and leaving over until Shabbos is only permitted if he does not act deceptively.

The Mishnah is authored by R. Shimon ben Elazar - as the Beraisa teaches - one may not prepare food on Yom Tov for after Yom Tov....

But a woman may fill a pot with meat, even though only one piece will be eaten; or (fill) a kettle of water even though only one cup will be drunk; but she may only bake bread that she actually needs.

Beraisa: R. Shimon ben Elazar says - A woman may fill her oven with bread (even though she does not need all of the loaves for Yom Tov) because the bread bakes well when the oven is full.

Rav Huna expounded the ruling of R. Shimon ben Elazar.

R. Yochanan expounded to the Tiverians like the ruling of R''SBE. He was actually expounding it merely as a Talmudic ruling but they understood that he was ruling that one may actually follow this Halachah.

Some explain that he told them to actually follow the ruling; they then came to ask him and he expounded it merely as a Talmudic ruling. He later expounded it again but they did not know whether it was a mere Talmudic ruling or an actual ruling that they could follow. (Note: A 'Talmudic ruling' refers to the conclusion of a Talmudic discussion which might not actually be the correct Halachah to follow.)

R. Aba bar Zavdi: R. Abahu instructed like the ruling of R''SBE.

R. Chiya quoting R. Yochanan: When a person makes the Eiruv he should say that it should be "for me and for anyone who did not make an Eiruv''.

If a person did not make an Eiruv and no-one else made it for him, others that made an Eiruv for themselves may make him food from his own ingredients.

R. Zerikan quoting R. Zeira: It is only permitted if he gives e.g. the flour to them as a gift ; otherwise they are cooking for him from his property, which is prohibited.