Corollary 4.3.7.14. Let $X$ be a Kan complex containing a vertex $x$. Then the simplicial sets $X_{/x}$ and $X_{x/}$ are contractible Kan complexes.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Corollary 4.3.7.13 in the special case $S = \Delta ^{0}$. $\square$