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Theorem tgptps 17763
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 17762 . 2  |-  ( G  e.  TopGrp  ->  G  e. TopMnd )
2 tmdtps 17759 . 2  |-  ( G  e. TopMnd  ->  G  e.  TopSp )
31, 2syl 15 1  |-  ( G  e.  TopGrp  ->  G  e.  TopSp )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   TopSpctps 16634  TopMndctmd 17753   TopGrpctgp 17754
This theorem is referenced by:  tgptopon  17765  istgp2  17774  tsmsinv  17830  tsmssub  17831  tgptsmscls  17832  tgptsmscld  17833  tsmsxplem1  17835  tsmsxp  17837  trgtps  17852  nrgtrg  18200
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-nul 4149
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-tmd 17755  df-tgp 17756
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