Suppose that $p:E \to B$ and $q:B \to B'$ are fibrations. Is it true that $qp:E \to B'$ is a fibration?
I thought this might just be 'abstract-nonsense'. There is a diagram (possibly correct?) that looks like
which is basically just the two fibrations, but I can't seem to construct a map $H:X \times I \to E$