Now we come to the topic of Eiruv Tavshilin:

Mishnah:

If Yom Tov falls out on Friday, you cannot cook on Yom Tov for Shabbos. You can cook for Yom Tov, and if there’s anything left over, it may be used on Shabbos.

If you cook something [for Shabbos] before Yom Tov, you can rely on it for Shabbos [this item that you cooked on Thursday becomes an “Eruv Tavshilin” - it’s your food for Shabbos, and then you can continue cooking on Friday (Yom Tov) for Shabbos; because you already have cooked food for Shabbos].
Beis Shammai: Two cooked items are necessary. Beis Hillel: One is enough. [One cooked item. But in order to bake, one baked item is necessary. For this reason we use a Matzah and an egg - a baked item and a cooked item]. They both agree that a fish with an egg cooked on it is considered two cooked items.
If he ate it [the Eruv] or it was lost, it cannot be relied on. If something [at least a kzayis] was left over, he can rely on it and cook for Shabbos.

Gemara:

Question: From where do we know these things [the Gemara will quote pesukim. Rashi explains that eruv is obviously a takanah of Chazal. The pesukim are quoted as a source for the necessity of Eruv]?

Shmuel: The verse states “Keep in mind to sanctify the Shabbos”, Shabbos must especially be kept in mind when another day [Yom Tov] comes that will make you forget.

Question: What’s the reason [that it is necessary to make an Eruv Tavshilin]?

Rava: So that he should choose a good portion for Shabbos just like he does for Yom Tov.

Rav Ashi: To remind people that it is forbidden to cook for Shabbos on Yom Tov, and certainly not for the weekdays.

Challenge: We learned in the Mishnah: “If you cook something [for Shabbos] before Yom Tov, you can rely on it for Shabbos”. According to Rav Ashi we understand why it must be done before Yom Tov. But according to Rava, why can’t it be done on Yom Tov?Resolution: You’re right. Only we’re concerned he may forget on Yom Tov [due to feasting and inebriation]. 

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