Theorem elmapd

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

	Ref	Expression
Hypotheses	elmapd.a	$$⊢\phi \to A\in V$$
	elmapd.b	$$⊢\phi \to B\in W$$
Assertion	elmapd	$$⊢\phi \to \left(C\in \left(A^B\right)\leftrightarrow C:B⟶A\right)$$

Proof

Step	Hyp	Ref	Expression
1		elmapd.a	$$⊢\phi \to A\in V$$
2		elmapd.b	$$⊢\phi \to B\in W$$
3		elmapg	$$⊢\left(A\in V\wedge B\in W\right)\to \left(C\in \left(A^B\right)\leftrightarrow C:B⟶A\right)$$
4	1 2 3	syl2anc	$$⊢\phi \to \left(C\in \left(A^B\right)\leftrightarrow C:B⟶A\right)$$