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Theorem t1top 17058
Description: A T1 space is a topological space. (Contributed by Jeff Hankins, 1-Feb-2010.)
Assertion
Ref Expression
t1top  |-  ( J  e.  Fre  ->  J  e.  Top )

Proof of Theorem t1top
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 eqid 2283 . . 3  |-  U. J  =  U. J
21ist1 17049 . 2  |-  ( J  e.  Fre  <->  ( J  e.  Top  /\  A. x  e.  U. J { x }  e.  ( Clsd `  J ) ) )
32simplbi 446 1  |-  ( J  e.  Fre  ->  J  e.  Top )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   A.wral 2543   {csn 3640   U.cuni 3827   ` cfv 5255   Topctop 16631   Clsdccld 16753   Frect1 17035
This theorem is referenced by:  t1t0  17076  lpcls  17092  perfcls  17093  restt1  17095  t1sep2  17097  sst1  17102  t1conperf  17162  t1hmph  17482  onint1  24888
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
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-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  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-t1 17042
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