We mentioned that there is Al hanissim in davening, but what about during birchas Hamazon? It’s only drabanan so maybe there’s no need but there is an aspect of פרסומי ניסא. The Gemara says one doesn’t “need” to, but if done, it should be during נודה and not רצה.

Once it’s concluded that one doesn’t have to say al Hanisim in Birchas Hamazon, the Gemara wonders about yaalev vyavo during Birchas Hamazon on Rosh Chodesh. (Rosh Chodesh is from the Torah but it’s not assur in work) It is a dispute but the Gemara favors the opinion that one must mention it.

On fast days there is the addition of עננו to davening. In the gemaras time, it was added to Maariv (night b4 the fast) shachris and Mincha.

Should we say Al Hanissim at Mussaf on Chanukah? (Like Shabbos or Rosh Chodesh) Chanukah isn’t “the cause” of Mussaf so maybe it can be omitted but on the other hand maybe once it’s a Tefillah said on Chanukah, it should have Al Hanissim. Ultimately, the Gemara says it should have Al Hanissim.

There are a few comparable cases that the Gemara discusses. They used to lain Haftorah by Shabbos Mincha but not on Yom Tov Mincha. So if it was both Shabbos and Yom Tov and they were laining Haftorah, should the Brachos include mention of Yom Tov. Another similar case is Yom Kippur that is also Shabbos. At Neilah, one should mention Shabbos as well.

There’s another case that the Gemara says is incomparable to Al Hanissim in Mussaf. We say Mini Chazaras Hashatz after Friday night Maariv. We do not say it after Yom Tov Maariv. If it’s both Shabbos and Yom Tov and we’re saying the mini Chazras Hashatz, we do NOT mention Yom tov. The reason is that to begin with, the mini Chazras Hashatz is not essential. It was added to davening to make sure no latecomer would walk home alone.

Terumah that is tamei has a mitzvah for it to be burned. However, on Yom tov one cannot fulfill that mitzvah and burn oil of Terumah that became tamei, bc one can’t burn on Yom Tov unless it’s dedicated for food. Even though we have a principle that a mitzvah pushes away an aveira, we do not use that principle here as derived from various Pesukim. Additionally, refraining from work on Yom Tov may also be a positive mitzvah and a mitzvah certainly can’t push away a negative and positive mitzvah.