The Stacks project

Proof. Let $i : X \to Y$ be an immersion of algebraic spaces. Choose a scheme $V$ and a surjective étale morphism $V \to Y$. Then $V \times _ Y X \to V$ is an immersion of schemes, hence unramified (see Morphisms, Lemmas 29.35.7 and 29.35.8). Thus by definition $i$ is unramified. $\square$

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