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 × V ) )

Proof

Step	Hyp	Ref	Expression
1		cnvcnv	⊢ ◡ ◡ 𝐴 = ( 𝐴 ∩ ( V × V ) )
2	1	difeq2i	⊢ ( 𝐴 ∖ ◡ ◡ 𝐴 ) = ( 𝐴 ∖ ( 𝐴 ∩ ( V × V ) ) )
3		difin	⊢ ( 𝐴 ∖ ( 𝐴 ∩ ( V × V ) ) ) = ( 𝐴 ∖ ( V × V ) )
4	2 3	eqtri	⊢ ( 𝐴 ∖ ◡ ◡ 𝐴 ) = ( 𝐴 ∖ ( V × V ) )