Charles Ellicott Commentary Numbers 3:13

"for all the first-born are mine; on the day that I smote all the first-born in the land of Egypt I hallowed unto me all the first-born in Israel, both man and beast; mine they shall be: I am Jehovah." — Numbers 3:13 (ASV)

On the day that I smote all the firstborn. —The command given to Moses regarding the sanctification or separation of the firstborn, of both humans and animals, is recorded immediately after the account of the exodus and of the institution of the Passover (Exodus 13:1–2). It is not clear, however, from the terms used whether the sanctification or separation applied to the firstborn then in existence—which appears to be by far the more probable view—or whether, as some suppose, the command was simply prospective. The whole nation of Israel is described in Exodus 4:22 as the Lord’s firstborn son, and the firstborn sons appear to have been regarded as representatives of the entire nation.

Mine shall they be: I am the Lord. —Or, They shall be (that is, belong) to me, (even) to me, Jehovah. (Compare Genesis 4:26: And to Seth, to him also. Literally, And to Seth, even him.)