Kerodon

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

Exercise 5.3.6.2. Let $\operatorname{\mathcal{C}}$ be a simplicial set and let $W$ be a collection of edges of $\operatorname{\mathcal{C}}$ which has the two-out-of-six property. Show that $W$ has the two-out-of-three property. That is, for any $2$-simplex $\sigma $ of $\operatorname{\mathcal{C}}$, if any two of the faces $d_0(\sigma )$, $d_1(\sigma )$, and $d_2(\sigma )$ belong to $W$, then so does the third.