Theorem ffn

Description: A mapping is a function with domain. (Contributed by NM, 2-Aug-1994)

	Ref	Expression
Assertion	ffn	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 Fn 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		df-f	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 ↔ ( 𝐹 Fn 𝐴 ∧ ran 𝐹 ⊆ 𝐵 ) )
2	1	simplbi	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 Fn 𝐴 )