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Theorem 0ntop 19866
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 3771 . 2  |-  -.  (/)  e.  (/)
2 0opn 19865 . 2  |-  ( (/)  e.  Top  ->  (/)  e.  (/) )
31, 2mto 179 1  |-  -.  (/)  e.  Top
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    e. wcel 1870   (/)c0 3767   Topctop 19848
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-v 3089  df-dif 3445  df-in 3449  df-ss 3456  df-nul 3768  df-pw 3987  df-sn 4003  df-uni 4223  df-top 19852
This theorem is referenced by:  istps  19882  ordcmp  30892  onint1  30894  kelac1  35626
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