Elements Are Sets, and the Empty Set and the Pair of Two Sets Exist and Are Unique

¶ Every element of a class is a set.

¶ There is exactly one set with no element, and every class with no element is equal to it.

¶ For all sets $x$ and $y$ there is exactly one set $z$ such that, for every set $u$, $u\in z$ if and only if $u=x$ or $u=y$.