Theorem cnvcnv2

Description: The double converse of a class equals its restriction to the universe. (Contributed by NM, 8-Oct-2007)

	Ref	Expression
Assertion	cnvcnv2	⊢ ◡ ◡ 𝐴 = ( 𝐴 ↾ V )

Proof

Step	Hyp	Ref	Expression
1		cnvcnv	⊢ ◡ ◡ 𝐴 = ( 𝐴 ∩ ( V × V ) )
2		df-res	⊢ ( 𝐴 ↾ V ) = ( 𝐴 ∩ ( V × V ) )
3	1 2	eqtr4i	⊢ ◡ ◡ 𝐴 = ( 𝐴 ↾ V )