Theorem elmapd

Description: Deduction form of elmapg . (Contributed by BJ, 11-Apr-2020)

	Ref	Expression
Hypotheses	elmapd.a	|- ( ph -> A e. V )
	elmapd.b	|- ( ph -> B e. W )
Assertion	elmapd	|- ( ph -> ( C e. ( A ^m B ) <-> C : B --> A ) )

Proof

Step	Hyp	Ref	Expression
1		elmapd.a	|- ( ph -> A e. V )
2		elmapd.b	|- ( ph -> B e. W )
3		elmapg	|- ( ( A e. V /\ B e. W ) -> ( C e. ( A ^m B ) <-> C : B --> A ) )
4	1 2 3	syl2anc	|- ( ph -> ( C e. ( A ^m B ) <-> C : B --> A ) )