Metamath Proof Explorer


Theorem ffnd

Description: A mapping is a function with domain, deduction form. (Contributed by Glauco Siliprandi, 17-Aug-2020)

Ref Expression
Hypothesis ffnd.1 ⊢ φ → F : A ⟶ B
Assertion ffnd ⊢ φ → F Fn A

Proof

Step Hyp Ref Expression
1 ffnd.1 ⊢ φ → F : A ⟶ B
2 ffn ⊢ F : A ⟶ B → F Fn A
3 1 2 syl ⊢ φ → F Fn A