Lemma 86.11.4. Let $S$ be a scheme. Let $X \to Z$ and $Y \to Z$ be morphisms of formal algebraic spaces over $S$. Then $(X \times _ Z Y)_{red} = (X_{red} \times _{Z_{red}} Y_{red})_{red}$.

**Proof.**
This follows from the universal property of the reduction in Lemma 86.8.1.
$\square$

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