Lemma 61.3.5. Let $A \to B$ be a local isomorphism. Then

$A \to B$ is étale,

$A \to B$ identifies local rings,

$A \to B$ is quasi-finite.

Lemma 61.3.5. Let $A \to B$ be a local isomorphism. Then

$A \to B$ is étale,

$A \to B$ identifies local rings,

$A \to B$ is quasi-finite.

**Proof.**
Omitted.
$\square$

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