Theorem ffrn

Description: A function maps to its range. (Contributed by Glauco Siliprandi, 3-Mar-2021)

	Ref	Expression
Assertion	ffrn	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 : 𝐴 ⟶ ran 𝐹 )

Proof

Step	Hyp	Ref	Expression
1		ffn	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 Fn 𝐴 )
2		dffn3	⊢ ( 𝐹 Fn 𝐴 ↔ 𝐹 : 𝐴 ⟶ ran 𝐹 )
3	1 2	sylib	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 : 𝐴 ⟶ ran 𝐹 )