Corollary 3

Tag 04A4, permanent. Cite it as [Bourbaki, Tag 04A4].

Commutative Algebra, chapter II, § 4. Spectra of rings and supports of modules

The set of minimal prime ideals of a Noetherian ring $A$ is finite.

$X = \mathrm{Spec}(A)$ has only a finite number of irreducible components (Corollary 7 to Proposition 11 and no. 2, Proposition 10) and the corollary follows from Corollary 2 above.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Remark, § 2

Cites

Corollary 7 to Proposition 11
Corollary 2