פירוש על ביצה 30:22

Our Mishna, On Yom Tov the initial cooking – The initial cooking on principle should be for Shabbat, rather than the initial cooking being for Yom Tov. The remainder can be for Shabbat, as we go on to teach, you can cook for Yom Tov without using a loophole, as taught later on.

Make a dish - for the purpose of the eruv.

And the egg upon it – the egg was on top of the fish when they fried it

Ate or lost – before he cooked all that was necessary for Shabbat

Rely on it – to cook for himself

From where are these words derived? – Not precisely learned from Scripture, the mixing of dishes is from the Rabbis. This is what the question is saying: What did the Rabbis cause it to rely on?

Remember – You only remember things that are liable to be forgotten.

From another that comes to make it forgotten – When Yom Tov falls on erev Shabbat, and it's close to Shabbat and will be forgotten because of Yom Tov, because you will be preparing a lot for the meal of the day, this doesn't allow for Shabbat to be honored, and the Scripture warns you to remember it (Shabbat). When you mix the mixed dishes, it turns out you will remember. You only do this for Shabbat.

What is the reason? – Why did (the Rabbis) ordain the eruv? The verse is certainly not speaking about the eruv, and the eruv is not heard from them, it is a mere support. When the verse comes, it teaches about saying Kiddush as it is taught in Masechet (tractate) Pesachim, remember Shabbat over wine. The eruv is from the Rabbis. What did they see to ordain this?

Rava said: select the choice portion – Since in the west, remember Shabbat and do not let Yom Tov consume everything. Choose a portion for this and a portion for that.

Rav Ashi says – They ordain it not on account of the honor of Shabbat, but rather the honor of Yom Tov.

So people will say "do not bake on Yom Tov for Shabbat" – unless the person begins to cook when it is still day, because then it is finishing what you started, but you cannot start.