Lemma 66.40.8. 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.