Theorem fnexd

Description: If the domain of a function is a set, the function is a set. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypotheses	fnexd.1	⊢ ( 𝜑 → 𝐹 Fn 𝐴 )
	fnexd.2	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
Assertion	fnexd	⊢ ( 𝜑 → 𝐹 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		fnexd.1	⊢ ( 𝜑 → 𝐹 Fn 𝐴 )
2		fnexd.2	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
3		fnex	⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐴 ∈ 𝑉 ) → 𝐹 ∈ V )
4	1 2 3	syl2anc	⊢ ( 𝜑 → 𝐹 ∈ V )