Corollary 4.1.4.8. Let $q: X \rightarrow S$ be an inner 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 an $\infty $-category.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 4.1.4.6 in the special case $A = \emptyset $. $\square$