(Rav and Shmuel): An egg laid on the first day of Rosh Hashanah is Asurah on the second, as indicated in the following Mishnah:

Out of concern that the Levi'im would (once again) say the wrong Shir, they instituted that they would not accept witnesses once the time came for the Minchah to be brought.

If witnesses did come after that time, both days would be treated as Kodesh (thus we find that the institution of two days for Rosh Hashanah was made by Beis Din, where it was not based on the doubtful day).

(Rabah): From R. Yochanan onwards the egg is permitted on the second day.

R. Yochanan re-allowed the witnesses to be accepted all day.

This was after the Churban when the concern for the Shir of the Levi'im is tragically not present.

From that point the two days of Rosh Hashanah are like any other, and are subject to the Mah Nafshach.

Question (Abaye): But Rav and Shmuel taught their prohibition after the Churban!?

Answer (Rabah): How can you ask me from the statements of Rav and Shmuel, given that I am speaking from the authority of the Tana, R. Yochanan b. Zakai!?

Question: But, indeed, how will Rav and Shmuel explain the Mishnah dealing with R. Yochanan's reinstitution?

Answer: The two days of Rosh Hashanah remained as they always were, Sefeikah d'Yoma, in Chutz La'Aretz (where Rav and Shmuel were ruling) and were unaffected by the various institutions in Eretz Yisrael (where the Din would, indeed, have changed).

Answer (R. Yosef): The egg would always be Asur, even in Eretz Yisrael, and even after R. Yochanan b. Zakai since the vote to prohibit the egg was never rescinded by a subsequent vote.

Question: How does R. Yosef know that a vote needs specific rescinding even after the cause for the original vote ends or is removed?

Answer: Hash-m rescinded the prohibitions surrounding Har Sinai, even though Matan Torah was over (citing two Pesukim, discussed below).

Alternate Answer: R. Eliezer only agreed to redeem his Kerem Rivai after R. Yochanan voted to repeal the requirement to bring the (nearby) fruits to Yerushalayim, even though the rationale for bringing the fruits (adorning the markets of Yerushalayim with bounty) was no longer present.

Question: Why did R. Yosef cite two Pesukim in his first answer and then give a second answer?

Answer: All are needed.

The first Pasuk might be understood only to instruct the People to return to their wives for Mitzvas Onah, but not to permit that which had become obviously permitted (while the second Pasuk gives permission to ascend Har Sinai).

The Pesukim regarding Har Sinai might only apply to d'Oraisa "votes" while the second answer shows that even a d'Rabanan is binding until there is a vote of repeal.

Question: Perhaps R. Yochanan b. Zakai voted to permit the egg, as well!?

Answer: That is unlikely, since his Beis Din voted regarding testimony, and did not raise the egg issue.

Question (Abaye): Who said that egg is independent of testimony, such that its prohibition separately was voted on (perhaps it simply follows the rules of testimony)!?

Answer (R. Ada and R. Salman): The actual reason for the permanent Isur of the egg is lest people apply the wrong Din when the Beis ha'Mikdash is soon restored.

Question: Then we should not permit the witnesses after Mincha either!?

Answer: Beis Din is more careful than people would be.

Answer (Rava): The egg is still prohibited since, even after R. Yochanan b. Zakai reaccepted the witnesses, there would still be two days of Yom Tov if they arrived after Mincha-time.

(Rava, in summary): The Halachah follows Rav (both l'Kula and l'Chumra) in the three cases cited.