Axiom of Infinity

There is a set $x$ such that the empty set $\emptyset$ satisfies $\emptyset\in x$ and, for every set $u$ with $u\in x$, there is a set $w$ with $w\in x$ whose elements are exactly the elements of $u$ together with $u$ itself; that is, for every set $s$, $s\in w$ if and only if $s\in u$ or $s=u$.