Lemma 88.23.9. In the situation above. If $X$ is locally Noetherian, $f$ is locally of finite type, and $U' \to U$ is étale, then $f_{/T}$ is rig-étale.

**Proof.**
The proof is exactly the same as the proof of Lemma 88.23.8 except with Lemmas 88.4.3 and 88.18.2 replaced by Lemmas 88.8.4 and 88.20.2
$\square$

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