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Metamath Proof Explorer

Theorem topnlly

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

Ref Expression
Assertion topnlly ⊢ N-Locally Top = Top

Proof

Step Hyp Ref Expression
1 toplly ⊢ Locally Top = Top
2 loclly ⊢ Locally Top = Top ↔ N-Locally Top = Top
3 1 2 mpbi ⊢ N-Locally Top = Top