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Theorem 0ntop 18651
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 3750 . 2  |-  -.  (/)  e.  (/)
2 0opn 18650 . 2  |-  ( (/)  e.  Top  ->  (/)  e.  (/) )
31, 2mto 176 1  |-  -.  (/)  e.  Top
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    e. wcel 1758   (/)c0 3746   Topctop 18631
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4522
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-v 3080  df-dif 3440  df-in 3444  df-ss 3451  df-nul 3747  df-pw 3971  df-sn 3987  df-uni 4201  df-top 18636
This theorem is referenced by:  istps  18674  ordcmp  28438  onint1  28440  kelac1  29565
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