Theorem elqs

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

	Ref	Expression
Hypothesis	elqs.1	|- B e. _V
Assertion	elqs	|- ( B e. ( A /. R ) <-> E. x e. A B = [ x ] R )

Proof

Step	Hyp	Ref	Expression
1		elqs.1	|- B e. _V
2		elqsg	|- ( B e. _V -> ( B e. ( A /. R ) <-> E. x e. A B = [ x ] R ) )
3	1 2	ax-mp	|- ( B e. ( A /. R ) <-> E. x e. A B = [ x ] R )