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Metamath Proof Explorer

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