The core question is whether an egg laid on Yom Tov that falls into a pladen full of permitted food, well over sixty times its volume, is nullified. Minchas Elazar (Chelek 1:1) holds that it is not nullified even in a thousand, because the egg was added to fix the dish (like water or salt in dough) and is therefore treated as a davar sheyesh lo matirin — since waiting until after Yom Tov would render it permitted on its own, the halacha prefers that the whole mixture be forbidden rather than nullified.
Kaf HaChayim (Orach Chayim 513:4-6) confirms this principle directly: an egg laid on Yom Tov that becomes mixed in, even with a thousand parts, is not nullified precisely because it is a davar sheyesh lo matirin — if left until after Yom Tov it reverts to permitted status on its own, and Chazal were stringent that one should rather wait than permit it through bitul.
The underlying prohibition on the egg itself traces to the law of muktzeh and nolad on Yom Tov: Rambam (Hilchot Yom Tov 1:18) rules that just as muktzeh is forbidden on Yom Tov, so is something that came into being (nolad) on that day, which is why an egg laid on Yom Tov cannot be eaten that day, and Be'er Heitev (Yoreh De'ah 102:4) cites this very egg as the classic example of a davar she-ye'atid lehיות mutar — something certain to become permitted afterward.
Bartenura (Mishnah Beitzah 1:1:1) explains the reasoning behind Beit Hillel's view that such an egg may not be eaten: any egg laid today was essentially completed the prior day, so permitting it would mean the preceding day prepared for Yom Tov, which is forbidden since one day may not prepare for another. Bartenura (Mishnah Eruvin 3:8:4) adds that if the first day is a weekday and the second day sacred, the egg is permitted on the second day since the weekday legitimately prepares for Yom Tov.
Rambam (Hilchot Chametz U'Matzah 15:6-9) and Lechem Mishneh (Hilchot Chametz U'Matzah 1:5:1) develop the broader principle of davar sheyesh lo matirin through the comparable case of chametz on Pesach, which is forbidden in any amount, in its own kind or otherwise, precisely because the mixture will become fully permitted after the festival — establishing the structural analogy Minchas Elazar draws upon for the egg case.
Chazon Ish (Orach Chayim 52) takes up a related practical question, whether something that fell into flour on Yom Tov may be removed by hand, noting that such removal is conceivable only on Yom Tov, when sorting for food preparation is permitted, whereas on Shabbat such removal would certainly constitute forbidden sorting.
Among later poskim addressing the egg laid on Yom Tov directly, B'tzel HaChochma (3:102) rules that in a place regularly frequented by chickens, an egg found there is permitted even without certainty that a chicken was present when it was laid, since its presence is presumed.
Tzitz Eliezer (5:8) addresses the scope of the prohibition itself, noting that according to the Rambam an egg laid on any weekday or Shabbat is only rabbinically forbidden, as a precautionary decree tied to Yom Tov adjacent to Shabbat, following the Arukh HaShulchan's explanation.
Har Tzvi (Yoreh De'ah 101) situates the egg within the broader rabbinic prohibition on produce that fell or liquids that flowed on Shabbat and Yom Tov, arguing that the egg is included in that decree even though the decree's original rationale does not strictly apply to an egg.
Avnei Yashfeh (7:41) rules that an egg whose laying on Yom Tov is in doubt is nonetheless forbidden as a davar sheyesh lo matirin, drawing on the parallel discussions in Yoreh De'ah, Orach Chayim, and the Mishnah Berurah.
