Corollary 3.1.3.14. Let $B$ be a simplicial set, let $A \subseteq B$ be a simplicial subset, and let $f: A \rightarrow X$ be a morphism of simplicial sets. If $X$ is a Kan complex, then the simplicial set $\operatorname{Fun}_{A/}(B, X)$ is a Kan complex. If the inclusion $A \hookrightarrow B$ is anodyne, then the Kan complex $\operatorname{Fun}_{A/}(B, X)$ is contractible.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 3.1.3.13 in the special case $S = \Delta ^{0}$. $\square$