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The gemara in Pesachim 46b appears to contain an argument as to why it is biblically permitted to cook on yom tov for a shabbat which immediately follows it.

Rabbah implies that we need to rely on the principle of ho'il i.e. you can cook on yom tov for the purposes of shabbat, since you may actually need the food on yom tov, if guests unexpectedly turn up.

Rav Chisdah says that there is no need to use ho'il. It is completely permitted to prepare on shabbat for yom tov.

This is all on a biblical level. Rabinically, one needs an Eruv Tavshilin in order to cook on yom tov for shabbat (as discussed in Beitzah 15a).

Seemingly, according to Rabbah, even if one makes an Eruv Tavshilin, one would need to cook early enough on Friday to be able to use the food on yom tov itself, if guests were to turn up.

Is this really what Rabbah holds? Is this discussed by Rishonim?

If it is true, does anyone hold like Rabbah (or are they at least worried enough to take this position into account)? I'm looking for sources in classical or modern-day poskim that discuss how late one can cook on Friday with an Eruv Tavshilin.

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Mishnah Berurah 527:3 writes:

וכתבו האחרונים דביו"ט שחל להיות בע"ש יזהר להקדים הכנת מאכליו לשבת בכדי שיגמר מלאכתו בעוד יום גדול דסמוך לחשיכה בזמן דלא שייך שיצטרך לו ביו"ט גופא הלא יש כאן לתא דמלאכה דאורייתא ... וכתבו דמטעם זה נהגו להקדים תפלת ערבית בליל שבת כשחל סמוך ליו"ט כדי שלא יתאחר מלאכת בישולו ביום טוב עד סמוך לחשיכה

The Acharonim wrote that on Yom Tov which falls on Friday, one should be careful to prepare his food for Shabbat early enough that it can be completed while there is still much of the day left. Cooking close to when it gets dark, in such a way that it is not possible for him to use it on Yom Tov itself (i.e. before Shabbat) could involve a melacha de'oraita ... They wrote that for this reason we are accustomed to pray Ma'ariv early on Friday night when it falls immediately following Yom Tov, so that one won't delay his cooking on Yom Tov until close to dark.

Thus, Mishnah Berurah (following Magen Avraham 527:1) rules that one should follow Rabbah i.e. that cooking for Shabbat on Yom Tov with an Eruv Tavshilin needs to rely on ho'il and therefore should be completed early in the day.

However, he then refers the reader to what he wrote in Bi'ur Halachah, where he notes that there are many Rishonim on both sides of the question of whether the halachah is like Rabbah or Rav Chisdah.

His bottom line is:

וע"כ נראה דאף דלכתחלה בודאי צריך לזהר כדעת כל הני רבוותא הנ"ל ושהוא בענין דאורייתא וכמ"ש האחרונים מ"מ בשעת הדחק י"ל דכדאי הם רבותינו הראשונים האלה לסמוך עליהם בענין סמוך לחשיכה ... וכ"ש ביו"ט שני שהוא דרבנן בודאי יש לסמוך להקל לעת הצורך

Therefore it appears that although ideally one should be careful for the above-mentioned opinions of all our Rabbis [that one must finish cooking early enough before dark] as we are dealing with a de'oraita as the Acharonim wrote, nevertheless, in pressing circumstances, we can say that is is appropriate to rely on these [other] Rishonim to cook close to dark ... And certainly when Friday is Yom Tov Sheini [shel Galuyot] which is derabbanan, one can rely on the lenient opinion where necessary.

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