Lemma 99.4.6. Let $S$ be a scheme. The property of being quasi-DM over $S$, quasi-separated over $S$, or separated over $S$ (see Definition 99.4.2) is stable under change of base scheme, see Algebraic Stacks, Definition 92.19.3.

**Proof.**
Follows immediately from Lemma 99.4.4.
$\square$

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