Corollary 2

Let $\rho$ be a homomorphism of a ring $A$ to a ring $B$. If $E$ is a flat right $A$-module, the right $B$-module $\rho^*(E) = E_{(B)}$ obtained by extending the ring of scalars to $B$ (Algebra*, Chapter II, § 5, no. 1) is flat.*

By definition $E_{(B)} = E \otimes_A B$, where $B$ is considered as an $(A,B)$-bimodule by means of $\rho$. As the right $B$-module $B_d$ is flat, it is sufficient to apply Proposition 8.