Corollary 5.7.7.5. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets. Then $U$ is an isofibration.

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 5.7.7.5. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets. Then $U$ is an isofibration.

**Proof.**
By virtue of Corollary 5.7.7.3, we may assume without loss of generality that $U$ is a cocartesian fibration of $\infty $-categories, in which case the desired result follows from Proposition 5.1.4.8.
$\square$