 Existence of classes: If \(\phi(x)\) is any formula, then the class \(\phi(x)\) of all sets \(x\) such that \(\phi(x)\) exists. (The set \(x\) is identified with the class of elements of \(x\).) Note that Kuratowski pairs of sets are sets, and so we can define (class) relations and functions on the universe of sets much as usual.