Axiom of Pairing
The Axiom of Pairing is a possible axiom in Material set theory: zf
which is to say, for any two objects (possibly the same) there is a set whose only elements are those two objects.
It follows from the Axiom of Extensionality that such a doubleton
Axiom of Pairing for classes
In a material set theory with classes, we must modify the axiom slightly, since we cannot pair proper classes: nbg