Theorem opelcnv

Description: Ordered-pair membership in converse relation. (Contributed by NM, 13-Aug-1995)

	Ref	Expression
Hypotheses	opelcnv.1	|- A e. _V
	opelcnv.2	|- B e. _V
Assertion	opelcnv	|- ( <. A , B >. e. `' R <-> <. B , A >. e. R )

Proof

Step	Hyp	Ref	Expression
1		opelcnv.1	|- A e. _V
2		opelcnv.2	|- B e. _V
3		opelcnvg	|- ( ( A e. _V /\ B e. _V ) -> ( <. A , B >. e. `' R <-> <. B , A >. e. R ) )
4	1 2 3	mp2an	|- ( <. A , B >. e. `' R <-> <. B , A >. e. R )