Corollary 7.2.3.13. Suppose we are given a pullback diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}' \ar [d] \ar [r]^-{F} & \operatorname{\mathcal{C}}\ar [d]^-{\pi } \\ \operatorname{\mathcal{D}}' \ar [r]^-{\overline{F}} & \operatorname{\mathcal{D}}. } \]
If $\pi $ is a cocartesian fibration and $\overline{F}$ is right anodyne, then $F$ is right anodyne.