Corollary 3.1.3.15. Let $q: X \rightarrow S$ be a Kan fibration of simplicial sets, and let $g: B \rightarrow S$ be any morphism of simplicial sets. Then the simplicial set $\operatorname{Fun}_{/S}(B,X)$ is a Kan complex.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 3.1.3.13 in the special case $A = \emptyset $. $\square$