Corollary 3
Tag 04EK, permanent. Cite it as [Bourbaki, Tag 04EK].
Commutative Algebra, chapter III, § 2. General results on filtered rings and modules
If C is a commutative Noetherian ring, every finitely generated commutative C-algebra is a Noetherian ring.
Such an algebra is isomorphic to a quotient of a polynomial algebra C[X_1, ..., X_n] (§ 1, no. 1).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.