Corollary 1 (Hilbert’s Theorem)
Tag 04EI, permanent. Cite it as [Bourbaki, Tag 04EI].
Commutative Algebra, chapter III, § 2. General results on filtered rings and modules
For every commutative Noetherian ring C, the polynomial ring C[X] is Noetherian (cf. Exercise 10).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.