Lemma 42.22.3. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X' \to X$ be a morphism of schemes locally of finite type over $S$. If $f : Y \to X$ is an envelope, then the base change $f' : Y' \to X'$ of $f$ is an envelope too.

Proof. Follows from Morphisms, Lemma 29.41.5 and More on Morphisms, Lemma 37.76.3. $\square$

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