Theorem elmaprd

Description: Deduction associated with elmapd . Reverse direction of elmapdd . (Contributed by Thierry Arnoux, 13-Oct-2025)

	Ref	Expression
Hypotheses	elmaprd.1	$$⊢\phi \to A\in V$$
	elmaprd.2	$$⊢\phi \to B\in W$$
	elmaprd.3	$$⊢\phi \to F\in \left(B^A\right)$$
Assertion	elmaprd	$$⊢\phi \to F:A⟶B$$

Proof

Step	Hyp	Ref	Expression
1		elmaprd.1	$$⊢\phi \to A\in V$$
2		elmaprd.2	$$⊢\phi \to B\in W$$
3		elmaprd.3	$$⊢\phi \to F\in \left(B^A\right)$$
4	2 1	elmapd	$$⊢\phi \to \left(F\in \left(B^A\right)\leftrightarrow F:A⟶B\right)$$
5	3 4	mpbid	$$⊢\phi \to F:A⟶B$$