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Metamath Proof Explorer

Theorem wunres

Description: A weak universe is closed under restrictions. (Contributed by Mario Carneiro, 12-Jan-2017)

Ref Expression
Hypotheses wun0.1 ⊢ φ → U ∈ WUni
wunop.2 ⊢ φ → A ∈ U
Assertion wunres ⊢ φ → A ↾ B ∈ U

Proof

Step Hyp Ref Expression
1 wun0.1 ⊢ φ → U ∈ WUni
2 wunop.2 ⊢ φ → A ∈ U
3 resss ⊢ A ↾ B ⊆ A
4 3 a1i ⊢ φ → A ↾ B ⊆ A
5 1 2 4 wunss ⊢ φ → A ↾ B ∈ U