Lemma 76.13.2. Let $S$ be a scheme. Let $a : F \to G$ be a transformation of functors $F, G : (\mathit{Sch}/S)_{fppf}^{opp} \to \textit{Sets}$. Then $a$ is formally étale if and only if $a$ is both formally smooth and formally unramified.
Proof. Formal from the definition. $\square$
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