This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fexd

Description: If the domain of a mapping is a set, the function is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypotheses fexd.1 ⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
fexd.2 ⊢ ( 𝜑 → 𝐴 ∈ 𝐶 )
Assertion fexd ( 𝜑 → 𝐹 ∈ V )

Proof

Step Hyp Ref Expression
1 fexd.1 ⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
2 fexd.2 ⊢ ( 𝜑 → 𝐴 ∈ 𝐶 )
3 fex ⊢ ( ( 𝐹 : 𝐴 ⟶ 𝐵 ∧ 𝐴 ∈ 𝐶 ) → 𝐹 ∈ V )
4 1 2 3 syl2anc ⊢ ( 𝜑 → 𝐹 ∈ V )