Lemma 10.150.10. Let $R$ be a local ring with henselization $R^ h$. Let $I \subset \mathfrak m_ R$. Then $R^ h/IR^ h$ is the henselization of $R/I$.
Henselization is compatible with quotients.
This is a special case of Lemma 10.150.9.
Proof. This is a special case of Lemma 10.150.9. $\square$
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