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Theorem ngptps 24615
Description: A normed group is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
ngptps (𝐺 ∈ NrmGrp → 𝐺 ∈ TopSp)

Proof of Theorem ngptps
StepHypRef Expression
1 ngpms 24613 . 2 (𝐺 ∈ NrmGrp → 𝐺 ∈ MetSp)
2 mstps 24465 . 2 (𝐺 ∈ MetSp → 𝐺 ∈ TopSp)
31, 2syl 17 1 (𝐺 ∈ NrmGrp → 𝐺 ∈ TopSp)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108  TopSpctps 22938  MetSpcms 24328  NrmGrpcngp 24590
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-xp 5691  df-co 5694  df-res 5697  df-iota 6514  df-fv 6569  df-xms 24330  df-ms 24331  df-ngp 24596
This theorem is referenced by:  nmcn  24866  cnmpt1ip  25281  cnmpt2ip  25282  csscld  25283  clsocv  25284  rrxtps  46301
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