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Theorem 0ntop 16651
Description: The empty set is not a topology. (Contributed by FL, 1-Jun-2008.)
Assertion
Ref Expression
0ntop  |-  -.  (/)  e.  Top

Proof of Theorem 0ntop
StepHypRef Expression
1 noel 3459 . 2  |-  -.  (/)  e.  (/)
2 0opn 16650 . 2  |-  ( (/)  e.  Top  ->  (/)  e.  (/) )
31, 2mto 167 1  |-  -.  (/)  e.  Top
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1684   (/)c0 3455   Topctop 16631
This theorem is referenced by:  istps  16674  ordcmp  24886  onint1  24888  topnem  25512  kelac1  27161
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-sep 4141
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  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-ne 2448  df-ral 2548  df-rex 2549  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-sn 3646  df-uni 3828  df-top 16636
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