Proposition 11.6.0.135. Let $i: A_{} \hookrightarrow B_{}$ be an anodyne morphism of simplicial sets and let $f: X_{} \rightarrow S_{}$ be a Kan fibration. Then the induced map
\[ \operatorname{Fun}( B_{}, X_{} ) \rightarrow \operatorname{Fun}( B_{}, S_{} ) \times _{ \operatorname{Fun}( A_{}, S_{} )} \operatorname{Fun}( A_{}, X_{} ) \]
is a trivial Kan fibration.