Who were the "Kohanim" to whom the Pasuk is referring?
Rashi (citing Zevachim 115b), R. Bachye #1, and Rashbam: The Bechoros, who performed the Avodah until Aharon and his sons were chosen.
R. Bachye #2 and Hadar Zekenim: The descendants of Aharon (Nadav and Avihu - Zevachim 115b) 1 - since they were destined to become Kohanim later - R. Bachye). 2
See Torah Temimah, note 44. Refer also to 19:22:151:1.
R. hidekel 'hu ha'Holech Kidmas Ashur" - even though Ashur did not yet exist.
What are the connotations of ha'Kohanim ha'Nigashim el Hashem?
Rashi, Ramban, R. Bachye, Targum Onkelos and Targum Yonasan: It means the Kohanim, who perform the Avodah, who come close to Hashem to bring their Korbanos (to serve Him - Targum Onkelos and Targum Yonasan).
Why might the Kohanim think that they were permitted to ascend the mountain?
Rashi: Because they come close to Hashem when they sacrifice Korbanos.
Refer to 19:21:1:4 .
What are the connotations of "Pen Yifrotz bahem Hashem"?
Rashi: 'Lest Hashem - creates a breach in their ranks' - by killing some of them.
Targum Onkelo and Targum Yonasan: 'Lest Hashem kill some of them'.
Seeing as, in Pasuk 24, the Torah writes "Pen Yifrotz Bam," why does it write here "Pen Yifrotz Bahem"? What is the significance of the extra 'Hey'?
