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Metamath Proof Explorer

Theorem mptexd

Description: If the domain of a function given by maps-to notation is a set, the function is a set. Deduction version of mptexg . (Contributed by Glauco Siliprandi, 24-Dec-2020)

Ref Expression
Hypothesis mptexd.1 ⊢ φ → A ∈ V
Assertion mptexd ⊢ φ → x ∈ A ⟼ B ∈ V

Proof

Step Hyp Ref Expression
1 mptexd.1 ⊢ φ → A ∈ V
2 mptexg ⊢ A ∈ V → x ∈ A ⟼ B ∈ V
3 1 2 syl ⊢ φ → x ∈ A ⟼ B ∈ V