Theorem pwvabrel

Description: The powerclass of the cartesian square of the universal class is the class of all sets which are binary relations. (Contributed by BJ, 21-Dec-2023)

	Ref	Expression
Assertion	pwvabrel	|- ~P ( _V X. _V ) = { x | Rel x }

Proof

Step	Hyp	Ref	Expression
1		pwvrel	|- ( x e. _V -> ( x e. ~P ( _V X. _V ) <-> Rel x ) )
2	1	elv	|- ( x e. ~P ( _V X. _V ) <-> Rel x )
3	2	eqabi	|- ~P ( _V X. _V ) = { x | Rel x }