Lemma 10.126.11. Let $R$ be a ring. Let $I \subset R$ be an ideal. Let $S \to S'$ be an $R$-algebra map. Assume that
$I$ is locally nilpotent,
$S/IS \to S'/IS'$ is an isomorphism,
$S$ is of finite type over $R$,
$S'$ of finite presentation over $R$, and
$S'$ is flat over $R$.
Then $S \to S'$ is an isomorphism.