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Theorem 0ntop 16667
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 3472 . 2  |-  -.  (/)  e.  (/)
2 0opn 16666 . 2  |-  ( (/)  e.  Top  ->  (/)  e.  (/) )
31, 2mto 167 1  |-  -.  (/)  e.  Top
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1696   (/)c0 3468   Topctop 16647
This theorem is referenced by:  istps  16690  ordcmp  24958  onint1  24960  topnem  25615  kelac1  27264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-nul 3469  df-pw 3640  df-sn 3659  df-uni 3844  df-top 16652
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