Exercise 2, § 7

Let $A$ be a noetherian ring, $J$ an ideal of $A$ and $\widehat{A}$ the separated completion of $A$ for the $J$-adic topology. If the $A$-algebra $\widehat{A}$ is formally smooth (for the discrete topology), it is formally étale (observe that one has $\Omega_A(\widehat{A}) = J^n \Omega_A(\widehat{A})$ for every integer $n$).