Metamath Proof Explorer

Theorem llytop

Description: A locally A space is a topological space. (Contributed by Mario Carneiro, 2-Mar-2015)

Ref Expression
Assertion llytop ⊢ J ∈ Locally A → J ∈ Top

Proof

Step Hyp Ref Expression
1 islly ⊢ J ∈ Locally A ↔ J ∈ Top ∧ ∀ x ∈ J ∀ y ∈ x ∃ u ∈ J ∩ 𝒫 x y ∈ u ∧ J ↾ 𝑡 u ∈ A
2 1 simplbi ⊢ J ∈ Locally A → J ∈ Top