Theorem elrn

Description: Membership in a range. (Contributed by NM, 2-Apr-2004)

	Ref	Expression
Hypothesis	elrn.1	|- A e. _V
Assertion	elrn	|- ( A e. ran B <-> E. x x B A )

Proof

Step	Hyp	Ref	Expression
1		elrn.1	|- A e. _V
2		elrng	|- ( A e. _V -> ( A e. ran B <-> E. x x B A ) )
3	1 2	ax-mp	|- ( A e. ran B <-> E. x x B A )