Metamath Proof Explorer


Theorem elmaprd

Description: Deduction associated with elmapd . Reverse direction of elmapdd . (Contributed by Thierry Arnoux, 13-Oct-2025) Removed redundant hypotheses. (Revised by SN, 30-Aug-2026)

Ref Expression
Hypothesis elmaprd.1
|- ( ph -> F e. ( B ^m A ) )
Assertion elmaprd
|- ( ph -> F : A --> B )

Proof

Step Hyp Ref Expression
1 elmaprd.1
 |-  ( ph -> F e. ( B ^m A ) )
2 elmapi
 |-  ( F e. ( B ^m A ) -> F : A --> B )
3 1 2 syl
 |-  ( ph -> F : A --> B )