Corollary 2
Tag 04EJ, permanent. Cite it as [Bourbaki, Tag 04EJ].
Commutative Algebra, chapter III, § 2. General results on filtered rings and modules
For every commutative Noetherian ring C and every integer , the polynomial ring C[X1, ..., X_n] is Noetherian.*
This follows from Corollary 1 by induction on .
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.