Corollary 2

Let

${E'}^{f'}$ E

$p'p$

${B'}^f$ B

be a cartesian square. If $(E, p)$ is a locally trivial fibre B-space ( resp. a covering), then $(E', p')$ is a locally trivial fibre space ( resp. a covering) with base $B'$, trivializable if $(E, p)$ is.

This follows from corollary 1, applied with B = A and $E'= B'$.