Corollary 4.5.2.30. Suppose we are given a commutative diagram of $\infty $-categories
\[ \xymatrix { \operatorname{\mathcal{C}}_0 \ar [r]^{U} \ar [d] & \operatorname{\mathcal{C}}\ar [d] & \operatorname{\mathcal{C}}_1 \ar [l] \ar [d] \\ \operatorname{\mathcal{D}}_0 \ar [r]^{V} & \operatorname{\mathcal{D}}& \operatorname{\mathcal{D}}_1, \ar [l] } \]
where the vertical maps are equivalences of $\infty $-categories. If $U$ and $V$ are isofibrations, then the induced map $\operatorname{\mathcal{C}}_0 \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}_{1} \rightarrow \operatorname{\mathcal{D}}_0 \times _{\operatorname{\mathcal{D}}} \operatorname{\mathcal{D}}_1$ is an equivalence of $\infty $-categories.