Proposition 5

Let $\rho$ be a homomorphism from a ring $A$ to a ring $B$. If $E$ is a faithfully flat right $A$-module, the right $B$-module $\rho^*(E) = E_{(B)} = E \otimes_A B$ is faithfully flat.

Apply Proposition 4 of no. 2 with $R = A, S = F = B$, noting that the $B$-module $B_d$ is faithfully flat.