Corollary 2

*Let $k_0$ be a ring, $k$ a noetherian $k_0$-algebra formally smooth, and $B$ a $k$-algebra essentially of finite type. The set $U$ of prime ideals $\mathfrak{p}$ of $B$ such that the $k_0$-algebra $B_{\mathfrak{p}}$ is formally smooth (for the discrete topology or the $\mathfrak{p}B_{\mathfrak{p}}$-adic topology) is open in $\operatorname{Spec}(B)$ and the following conditions are equivalent:

(i) one has $U = \operatorname{Spec}(B)$ ; (ii) $U$ contains all the maximal ideals of $B$ ; (iii) the $k_0$*-algebra* $B$ is formally smooth.

This follows as above from Th. 3.