Metamath Proof Explorer


Theorem resexd

Description: The restriction of a set is a set. (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Hypothesis resexd.1 ⊢ φ → A ∈ V
Assertion resexd ⊢ φ → A ↾ B ∈ V

Proof

Step Hyp Ref Expression
1 resexd.1 ⊢ φ → A ∈ V
2 resexg ⊢ A ∈ V → A ↾ B ∈ V
3 1 2 syl ⊢ φ → A ↾ B ∈ V