Lemma 29.35.4. The base change of a morphism which is étale is étale.
Proof. In the proof of Lemma 29.35.2 we saw that being étale is a local property of ring maps. Hence the lemma follows from Lemma 29.14.5 combined with the fact that being étale is a property of ring maps that is stable under base change, see Algebra, Lemma 10.142.3. $\square$
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