Theorem brco

Description: Binary relation on a composition. (Contributed by NM, 21-Sep-2004) (Revised by Mario Carneiro, 24-Feb-2015)

	Ref	Expression
Hypotheses	opelco.1	|- A e. _V
	opelco.2	|- B e. _V
Assertion	brco	|- ( A ( C o. D ) B <-> 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		brcog	|- ( ( A e. _V /\ B e. _V ) -> ( A ( C o. D ) B <-> E. x ( A D x /\ x C B ) ) )
4	1 2 3	mp2an	|- ( A ( C o. D ) B <-> E. x ( A D x /\ x C B ) )