  Let $\varphi\colon X\to Y$ be an affine continuous surjection between compact
convex sets. Suppose that the canonical copy of the space of real-valued affine
continuous functions on $Y$ in the space of real-valued affine continuous
functions on $X$ is complemented. We show that if $F$ is a topological vector
space, then $f\colon Y\to F$ is of affine Baire class $\alpha$ whenever the
composition $f\circ\varphi$ is of affine Baire class $\alpha$. This abstract
result is applied to extend known results on affine Baire classes of strongly
affine Baire mappings.
