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 )