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Theorem ngptps 20193
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 20191 . 2  |-  ( G  e. NrmGrp  ->  G  e.  MetSp )
2 mstps 20029 . 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 1756   TopSpctps 18500   MetSpcmt 19892  NrmGrpcngp 20169
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2720  df-rab 2723  df-v 2973  df-dif 3330  df-un 3332  df-in 3334  df-ss 3341  df-nul 3637  df-if 3791  df-sn 3877  df-pr 3879  df-op 3883  df-uni 4091  df-br 4292  df-opab 4350  df-xp 4845  df-co 4848  df-res 4851  df-iota 5380  df-fv 5425  df-xms 19894  df-ms 19895  df-ngp 20175
This theorem is referenced by:  nmcn  20420  cnmpt1ip  20758  cnmpt2ip  20759  csscld  20760  clsocv  20761
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