Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Proof. Let $K$ be a sifted simplicial set. Taking $I = \emptyset $ in Definition 10.1.1.1, we conclude that the projection map $K \rightarrow \Delta ^0$ is right cofinal, so that $K$ is weakly contractible by virtue of Proposition 7.2.1.5. $\square$