Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 3.3.7.2. Let $v: T \rightarrow S$ be a weak homotopy equivalence of simplicial sets. For every Kan fibration $f: X \rightarrow S$, the projection map $T \times _{S} X \rightarrow X$ is also a weak homotopy equivalence.