Lemma 15.52.6. Let $(A, \mathfrak m)$ be a Noetherian local ring. If $A$ is normal and the formal fibres of $A$ are normal (for example if $A$ is excellent or quasi-excellent), then $A^\wedge $ is normal.

**Proof.**
Follows immediately from Algebra, Lemma 10.163.8.
$\square$

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