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Theorem ngptps 21247
Description: A normed group is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
ngptps  |-  ( G  e. NrmGrp  ->  G  e.  TopSp )

Proof of Theorem ngptps
StepHypRef Expression
1 ngpms 21245 . 2  |-  ( G  e. NrmGrp  ->  G  e.  MetSp )
2 mstps 21083 . 2  |-  ( G  e.  MetSp  ->  G  e.  TopSp
)
31, 2syl 16 1  |-  ( G  e. NrmGrp  ->  G  e.  TopSp )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1819   TopSpctps 19523   MetSpcmt 20946  NrmGrpcngp 21223
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-opab 4516  df-xp 5014  df-co 5017  df-res 5020  df-iota 5557  df-fv 5602  df-xms 20948  df-ms 20949  df-ngp 21229
This theorem is referenced by:  nmcn  21474  cnmpt1ip  21812  cnmpt2ip  21813  csscld  21814  clsocv  21815
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