Corollary 5.6.7.5. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets. Then $U$ is an isofibration.

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

Corollary 5.6.7.5. 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 5.6.7.3, 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 5.1.4.9.
$\square$