Lemma 35.31.1. The property $\mathcal{P}(f)=$“$f$ is étale” is étale local on the source.

**Proof.**
Combine Lemma 35.26.4 with Morphisms, Lemma 29.36.2 (local for Zariski on source and target), Morphisms, Lemma 29.36.3 (pre-composing), and Lemma 35.14.4 (part (4)).
$\square$

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