Theorem bj-cnvcnv

Description: The double converse of a class strips out all elements that are not ordered pairs. (Contributed by NM, 8-Dec-2003) (Proof shortened by BJ, 26-Nov-2021) (Proof shortened by BJ, 16-Oct-2026) Prefer use of bj-cnvcnv2 . (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-cnvcnv	|- `' `' A = ( A i^i ( _V X. _V ) )

Proof

Step	Hyp	Ref	Expression
1		bj-cnvcnv2	|- `' `' A = ( A |` _V )
2		df-res	|- ( A |` _V ) = ( A i^i ( _V X. _V ) )
3	1 2	eqtri	|- `' `' A = ( A i^i ( _V X. _V ) )