Theorem opelco

Description: Ordered pair membership in a composition. (Contributed by NM, 27-Dec-1996) (Revised by Mario Carneiro, 24-Feb-2015)

	Ref	Expression
Hypotheses	opelco.1	|- A e. _V
	opelco.2	|- B e. _V
Assertion	opelco	|- ( <. A , B >. e. ( C o. D ) <-> E. x ( A D x /\ x C B ) )

Proof

Step	Hyp	Ref	Expression
1		opelco.1	|- A e. _V
2		opelco.2	|- B e. _V
3		df-br	|- ( A ( C o. D ) B <-> <. A , B >. e. ( C o. D ) )
4	1 2	brco	|- ( A ( C o. D ) B <-> E. x ( A D x /\ x C B ) )
5	3 4	bitr3i	|- ( <. A , B >. e. ( C o. D ) <-> E. x ( A D x /\ x C B ) )