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Theorem tgptps 18025
Description: A topological group is a topological space. (Contributed by FL, 21-Jun-2010.) (Revised by Mario Carneiro, 13-Aug-2015.)
Assertion
Ref Expression
tgptps  |-  ( G  e.  TopGrp  ->  G  e.  TopSp )

Proof of Theorem tgptps
StepHypRef Expression
1 tgptmd 18024 . 2  |-  ( G  e.  TopGrp  ->  G  e. TopMnd )
2 tmdtps 18021 . 2  |-  ( G  e. TopMnd  ->  G  e.  TopSp )
31, 2syl 16 1  |-  ( G  e.  TopGrp  ->  G  e.  TopSp )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1717   TopSpctps 16878  TopMndctmd 18015   TopGrpctgp 18016
This theorem is referenced by:  tgptopon  18027  istgp2  18036  tsmsinv  18092  tsmssub  18093  tgptsmscls  18094  tgptsmscld  18095  tsmsxplem1  18097  tsmsxp  18099  trgtps  18114  nrgtrg  18590
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2362  ax-nul 4273
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2236  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2506  df-ne 2546  df-ral 2648  df-rex 2649  df-rab 2652  df-v 2895  df-sbc 3099  df-dif 3260  df-un 3262  df-in 3264  df-ss 3271  df-nul 3566  df-if 3677  df-sn 3757  df-pr 3758  df-op 3760  df-uni 3952  df-br 4148  df-iota 5352  df-fv 5396  df-ov 6017  df-tmd 18017  df-tgp 18018
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