Lemma 10.154.1. Let $R \to A$ and $R \to R'$ be ring maps. If $A$ is a filtered colimit of étale ring maps, then so is $R' \to R' \otimes _ R A$.

**Proof.**
This is true because colimits commute with tensor products and étale ring maps are preserved under base change (Lemma 10.143.3).
$\square$

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