- פסח בשאר ימות השנה שלמים נינהו re: being valid שלא לשמו
On the previous Daf, Rav Huna asserted that there cannot be a korban which is invalid when shechted לשמו, but is valid when shechted לא לשמו. The Gemara objects that there is such a korban: והרי פסח בשאר ימות השנה – but there is the case of a korban pesach during the other days of the year (i.e., before erev Pesach), which is not valid if it was shechted לשמו (as a pesach), but is valid if it was shechted שלא לשמו!? The Gemara answers: פסח בשאר ימות השנה שלמים נינהו – a pesach during the other days of the year is considered a shelamim. Since it is considered a שלמים then, it is thus valid when shechted "לשמו", i.e., as a שלמים.
- When was the avodah taken from the בכורות and given to Kohanim?
Rav Huna bar Rav Ketina was once sitting before Rav Chisda, who read the passuk וישלח את נערי בני ישראל – and he sent the youths of the children of Yisroel, explaining it to refer to the firstborn. Rav Huna told him that Rebbe Assi said: ופסקו – and they ceased thereafter; after this final avodah of the בכורות, the Kohanim would perform it from then on. Rav Chisda challenged him from a Baraisa teaching that until the משכן was erected, במות were permitted, and avodah was performed by בכורות. All kosher animals could be sacrificed, including חיות – wild animals, males and females, and בעלי מומין – blemished [animals], all of which were brought as עולות, and they required הפשט and ניתוח. The Gemara answers that Tannaim debate who performed avodah between the giving of the Torah and the משכן’s erection. The passuk says: וגם הכהנים הנגשים אל ה' יתקדשו – and also the “Kohanim” who come close to Hashem should prepare themselves (i.e., keep their distance from the mountain like all Jews). Rebbe Yehoshua ben Korchah says: זו פרישות בכורות – this refers to the separating from the mountain of the firstborns, who performed the avodah then. Rebbe says it refers to נדב and אביהו, i.e., Kohanim, who performed avodah from then on.
- Hashem was sanctified through the deaths of Nadav and Avihu
When Aharon’s sons died, Moshe told him: הוא אשר דבר ה' לאמר בקרובי אקדש – this is what Hashem spoke, saying: “I will be sanctified by those nearest Me.” This can refer to the above warning to keep a distance from the mountain, or that Hashem foretold of their deaths when He told Moshe, “I will set My meeting place there (in the משכן) with the children of Yisroel, ונקדש בכבודי – and it will be sanctified through My honor.” Do not read it as "בכבודי", rather, as במכובדיי – through my honored ones. Moshe did understand this statement until Aharon’s sons died, at which time he said: אהרן אחי לא מתו בניך אלא להקדיש שמו של הקדוש ברוך הוא – My brother Aharon, your sons did not die except to sanctify Hashem’s Name, by demonstrating how Hashem punishes those closest to Him for relatively small misdeeds. When Aharon heard this, he was silent, and was rewarded for it. Similar messages are darshened from תהלים and משלי. Rebbe Yochanan quoted the passuk: נורא אלקים ממקדשך – You are awesome, Hashem, from Your sanctuaries. He said, do not read it as מקדשך, rather as ממקודשך – from Your sanctified ones, meaning: בשעה שעושה הקדוש ברוך הוא דין בקדושיו – when Hashem executes judgement against His holy ones, מתיירא ומתעלה ומתהלל – He becomes feared and exalted and praised.