Corollary
Tag 03MA, permanent. Cite it as [Bourbaki, Tag 03MA].
Theory of Sets, chapter III, § 5. Properties of integers
The number of permutations of a finite set with n elements is equal to n!.
For this number is equal to the number of injections of the set into itself (§ 4, no. 2, Proposition 2, Corollary 4).
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.