This comes from a comment made by user bof in this thread.

Let $X$ be a set, define ${\cal P}_2(X) = \big\{\{a, b\}: a\neq b\in X\big\}$.

Consider the statement

${\sf (S)}$ If $X$ is an infinite set, then there is a bijection $\varphi: {\cal P}_2(X)\to X$.

Does ${\sf (S)}$ imply ${\sf (AC)}$?