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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