Metamath Proof Explorer

Theorem ffi

Description: A function with finite domain is finite. (Contributed by Glauco Siliprandi, 11-Dec-2019)

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

Step	Hyp	Ref	Expression
1		ffn	$⊢ F : A ⟶ B \to F Fn A$
2		fnfi	$⊢ (F Fn A \land A \in Fin) \to F \in Fin$
3	1 2	sylan	$⊢ (F : A ⟶ B \land A \in Fin) \to F \in Fin$