Corollary 1
Tag 04ZA, permanent. Cite it as [Bourbaki, Tag 04ZA].
Commutative Algebra, chapter VII, § 1. Krull domains
In a Krull domain every non-zero prime ideal m contains a prime ideal of height 1. If m is not of height 1, then div m = 0 and A : m = A.
The first assertion has already been seen in the course of the proof of Theorem 3. If m is not of height 1 and p is a prime ideal of height 1 contained in m, then p ⊂ m̃ and p ≠ m̃; as div p is extremal, necessarily div m = div m̃ = 0; hence div(A : m) = 0 and, as A : m is divisorial (no. 1, Proposition 1), A : m = A.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.