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Theorem t0top 17393
Description: A T0 space is a topological space. (Contributed by Jeff Hankins, 1-Feb-2010.)
Assertion
Ref Expression
t0top  |-  ( J  e.  Kol2  ->  J  e. 
Top )

Proof of Theorem t0top
Dummy variables  x  y  o are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2436 . . 3  |-  U. J  =  U. J
21ist0 17384 . 2  |-  ( J  e.  Kol2  <->  ( J  e. 
Top  /\  A. x  e.  U. J A. y  e.  U. J ( A. o  e.  J  (
x  e.  o  <->  y  e.  o )  ->  x  =  y ) ) )
32simplbi 447 1  |-  ( J  e.  Kol2  ->  J  e. 
Top )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    e. wcel 1725   A.wral 2705   U.cuni 4015   Topctop 16958   Kol2ct0 17370
This theorem is referenced by:  restt0  17430  sst0  17437  kqt0  17778  t0hmph  17822  kqhmph  17851  ordtopt0  26192
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 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-uni 4016  df-t0 17377
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