Lemma 61.7.2. Let $A \to B$ and $A \to A'$ be ring maps. Let $B' = B \otimes _ A A'$ be the base change of $B$. If $A \to B$ is ind-étale, then $A' \to B'$ is ind-étale.

**Proof.**
This is Algebra, Lemma 10.154.1.
$\square$

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