Lemma 65.40.8. Let $S$ be a scheme. Let

be a commutative diagram of morphism of algebraic spaces over $S$. Assume

$X \to B$ is a proper morphism,

$Y \to B$ is separated and locally of finite type,

Then the scheme theoretic image $Z \subset Y$ of $h$ is proper over $B$ and $X \to Z$ is surjective.

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