Corollary 3.5.9.26. Let $X$ be an $n$-truncated Kan complex, let $k$ be an integer, and let $A$ be a $(k-1)$-connective simplicial set. Then the diagonal map $X \rightarrow \operatorname{Fun}(A, X)$ is $(n-k)$-truncated.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Corollary 3.5.9.25 in the special case $B = \Delta ^0$. $\square$