Theorem elmap

Description: Membership relation for set exponentiation. (Contributed by NM, 8-Dec-2003)

	Ref	Expression
Hypotheses	elmap.1	|- A e. _V
	elmap.2	|- B e. _V
Assertion	elmap	|- ( F e. ( A ^m B ) <-> F : B --> A )

Proof

Step	Hyp	Ref	Expression
1		elmap.1	|- A e. _V
2		elmap.2	|- B e. _V
3		elmapg	|- ( ( A e. _V /\ B e. _V ) -> ( F e. ( A ^m B ) <-> F : B --> A ) )
4	1 2 3	mp2an	|- ( F e. ( A ^m B ) <-> F : B --> A )