Theorem elcnv2

Description: Membership in a converse relation. Equation 5 of Suppes p. 62. (Contributed by NM, 11-Aug-2004)

	Ref	Expression
Assertion	elcnv2	|- ( A e. `' R <-> E. x E. y ( A = <. x , y >. /\ <. y , x >. e. R ) )

Proof

Step	Hyp	Ref	Expression
1		elcnv	|- ( A e. `' R <-> E. x E. y ( A = <. x , y >. /\ y R x ) )
2		df-br	|- ( y R x <-> <. y , x >. e. R )
3	2	anbi2i	|- ( ( A = <. x , y >. /\ y R x ) <-> ( A = <. x , y >. /\ <. y , x >. e. R ) )
4	3	2exbii	|- ( E. x E. y ( A = <. x , y >. /\ y R x ) <-> E. x E. y ( A = <. x , y >. /\ <. y , x >. e. R ) )
5	1 4	bitri	|- ( A e. `' R <-> E. x E. y ( A = <. x , y >. /\ <. y , x >. e. R ) )