The Stacks project

Lemma 29.41.5. The base change of a proper morphism is proper. The same is true for universally closed morphisms.

Proof. This is true by definition for universally closed morphisms. It is true for separated morphisms (Schemes, Lemma 26.21.12). It is true for morphisms of finite type (Lemma 29.15.4). Hence it is true for proper morphisms. $\square$

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