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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 )