Axiom:Axiom of Pairing/Set Theory/Strong Form

Axiom
For any two sets, there exists a set to which only those two sets are elements:


 * $\forall a: \forall b: \exists c: \forall z: \paren {z = a \lor z = b \iff z \in c}$

That is, let $a$ and $b$ be sets.

Then there exists a set $c$ such that $c = \set {a, b}$.

Thus it is possible to create a set whose elements are two sets that have already been created.

Also see

 * Equivalence of Formulations of Axiom of Pairing