Corollary 2
Tag 050Y, permanent. Cite it as [Bourbaki, Tag 050Y].
Commutative Algebra, chapter VII, § 2. Dedekind domains
The integral closure of in is a Dedekind domain.
This integral closure is an integrally closed Noetherian domain all of whose non-zero prime ideals are maximal; it suffices therefore to apply Theorem 1 of no. 2.
In particular:
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Nothing.