Theorem ffund

Description: A mapping is a function, deduction version. (Contributed by Glauco Siliprandi, 3-Mar-2021)

	Ref	Expression
Hypothesis	ffund.1	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
Assertion	ffund	⊢ ( 𝜑 → Fun 𝐹 )

Proof

Step	Hyp	Ref	Expression
1		ffund.1	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
2		ffun	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → Fun 𝐹 )
3	1 2	syl	⊢ ( 𝜑 → Fun 𝐹 )