Lemma 41.11.5. Let $Y$ be a locally Noetherian scheme. Let $f : X \to Y$ be locally of finite type. Let $x \in X$. The morphism $f$ is étale at $x$ in the sense of Definition 41.11.4 if and only if it is étale at $x$ in the sense of Morphisms, Definition 29.36.1.
Proof. This follows from Lemma 41.11.2 and the definitions. $\square$
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