Theorem elmaprdOLD

Description: Obsolete version of elmaprd as of 30-Aug-2026. (Contributed by Thierry Arnoux, 13-Oct-2025) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		elmaprdOLD.1	$$⊢\phi \to A\in V$$
2		elmaprdOLD.2	$$⊢\phi \to B\in W$$
3		elmaprdOLD.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	$$⊢\phi \to F:A⟶B$$