Metamath Proof Explorer

Theorem fex

Description: If the domain of a mapping is a set, the function is a set. (Contributed by NM, 3-Oct-1999)

		Ref	Expression
	Assertion	fex	$⊢ (F : A ⟶ B \land A \in C) \to F \in V$

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