Corollary 2
Tag 04ED, permanent. Cite it as [Bourbaki, Tag 04ED].
Commutative Algebra, chapter III, § 2. General results on filtered rings and modules
Let A be a complete Hausdorff filtered ring whose filtration is exhaustive. If gr(A) is a left Noetherian ring, so is A.
It is sufficient to apply Corollary 1 with E = A.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.