Lemma 15.11.10. Let $A$ be a ring and let $(A, I)$ and $(A, I')$ be henselian pairs. Then $(A, I + I')$ is an henselian pair.

**Proof.**
By Lemma 15.11.8 the pair $(A/I, (I' + I)/I)$ is henselian. Thus we get the conclusion from Lemma 15.11.9.
$\square$

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