Theorem elqsi

Description: Membership in a quotient set. (Contributed by NM, 23-Jul-1995)

	Ref	Expression
Assertion	elqsi	|- ( B e. ( A /. R ) -> E. x e. A B = [ x ] R )

Proof

Step	Hyp	Ref	Expression
1		elqsg	|- ( B e. ( A /. R ) -> ( B e. ( A /. R ) <-> E. x e. A B = [ x ] R ) )
2	1	ibi	|- ( B e. ( A /. R ) -> E. x e. A B = [ x ] R )