Metamath Proof Explorer

Theorem rnffi

Description: The range of a function with finite domain is finite. (Contributed by Glauco Siliprandi, 11-Dec-2019)

		Ref	Expression
	Assertion	rnffi	$⊢ (F : A ⟶ B \land A \in Fin) \to ran F \in Fin$

Step	Hyp	Ref	Expression
1		ffi	$⊢ (F : A ⟶ B \land A \in Fin) \to F \in Fin$
2		rnfi	$⊢ F \in Fin \to ran F \in Fin$
3	1 2	syl	$⊢ (F : A ⟶ B \land A \in Fin) \to ran F \in Fin$