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Theorem t1top 17386
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 2435 . . 3  |-  U. J  =  U. J
21ist1 17377 . 2  |-  ( J  e.  Fre  <->  ( J  e.  Top  /\  A. x  e.  U. J { x }  e.  ( Clsd `  J ) ) )
32simplbi 447 1  |-  ( J  e.  Fre  ->  J  e.  Top )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   A.wral 2697   {csn 3806   U.cuni 4007   ` cfv 5446   Topctop 16950   Clsdccld 17072   Frect1 17363
This theorem is referenced by:  t1t0  17404  lpcls  17420  perfcls  17421  restt1  17423  t1sep2  17425  sst1  17430  t1conperf  17491  t1hmph  17815  onint1  26191
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-t1 17370
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