Lemma 15.37.6. Let $R \to S$ be a ring map. Let $\mathfrak n \subset \mathfrak n' \subset S$ be ideals. If $R \to S$ is formally smooth for the $\mathfrak n$-adic topology, then $R \to S$ is formally smooth for the $\mathfrak n'$-adic topology.

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

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