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Theorem tgptps 20705
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 20704 . 2  |-  ( G  e.  TopGrp  ->  G  e. TopMnd )
2 tmdtps 20701 . 2  |-  ( G  e. TopMnd  ->  G  e.  TopSp )
31, 2syl 16 1  |-  ( G  e.  TopGrp  ->  G  e.  TopSp )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1819   TopSpctps 19524  TopMndctmd 20695   TopGrpctgp 20696
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  ax-nul 4586
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-eu 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  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-iota 5557  df-fv 5602  df-ov 6299  df-tmd 20697  df-tgp 20698
This theorem is referenced by:  tgptopon  20707  istgp2  20716  tsmsinv  20776  tsmssub  20777  tgptsmscls  20778  tgptsmscld  20779  tsmsxplem1  20781  tsmsxp  20783  trgtps  20798  nrgtrg  21324
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