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Metamath Proof Explorer

Theorem ngptps

Description: A normed group is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015)

Ref Expression
Assertion ngptps ( 𝐺 ∈ NrmGrp → 𝐺 ∈ TopSp )

Proof

Step Hyp Ref Expression
1 ngpms ⊢ ( 𝐺 ∈ NrmGrp → 𝐺 ∈ MetSp )
2 mstps ⊢ ( 𝐺 ∈ MetSp → 𝐺 ∈ TopSp )
3 1 2 syl ⊢ ( 𝐺 ∈ NrmGrp → 𝐺 ∈ TopSp )