Theorem nonrel

Description: A non-relation is equal to the base class with all ordered pairs removed. (Contributed by RP, 25-Oct-2020)

	Ref	Expression
Assertion	nonrel	|- ( A \ `' `' A ) = ( A \ ( _V X. _V ) )

Proof

Step	Hyp	Ref	Expression
1		cnvcnv	|- `' `' A = ( A i^i ( _V X. _V ) )
2	1	difeq2i	|- ( A \ `' `' A ) = ( A \ ( A i^i ( _V X. _V ) ) )
3		difin	|- ( A \ ( A i^i ( _V X. _V ) ) ) = ( A \ ( _V X. _V ) )
4	2 3	eqtri	|- ( A \ `' `' A ) = ( A \ ( _V X. _V ) )