Corollary 4.5.6.20. Let $\operatorname{\mathcal{C}}$ be a small category and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be an isofibrant diagram. Suppose that, for every object $C \in \operatorname{\mathcal{C}}$, the simplicial set $\mathscr {F}(C)$ is a Kan complex. Then the simplicial set $\varprojlim ( \mathscr {F} )$ is a Kan complex.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 4.5.6.19 in the special case $\mathscr {E} = \underline{ \Delta ^{0} }$. $\square$