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Metamath Proof Explorer

Theorem wunsn

Description: A weak universe is closed under singletons. (Contributed by Mario Carneiro, 2-Jan-2017)

Ref Expression
Hypotheses wununi.1 ⊢ φ → U ∈ WUni
wununi.2 ⊢ φ → A ∈ U
Assertion wunsn ⊢ φ → A ∈ U

Proof

Step Hyp Ref Expression
1 wununi.1 ⊢ φ → U ∈ WUni
2 wununi.2 ⊢ φ → A ∈ U
3 dfsn2 ⊢ A = A A
4 1 2 2 wunpr ⊢ φ → A A ∈ U
5 3 4 eqeltrid ⊢ φ → A ∈ U