The Stacks project

Proof. Let $f : X \to Y$ and $Y' \to Y$ be morphisms of formal algebraic spaces. Let $f' : X' \to Y'$ be the base change of $f$ by $Y' \to Y$. Then $\Delta _{X'/Y'}$ is the base change of $\Delta _{X/Y}$ by the morphism $X' \times _{Y'} X' \to X \times _ Y X$. Each of the properties of the diagonal used in Definition 87.30.1 is stable under base change. Hence the lemma is true. $\square$

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