Unordered Pairs Exist

Theorem
Let $A$ and $B$ be classes, which may be either sets or proper classes.

Then:
 * $\forall A, B: \left\{{A, B}\right\} \in U$

where $U$ is the universal class.

Also see

 * Axiom:Axiom of Pairing


 * Definition:Universal Class


 * Definition:Doubleton