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Theorem 0ntop 22800
Description: The empty set is not a topology. (Contributed by FL, 1-Jun-2008.)
Assertion
Ref Expression
0ntop ¬ ∅ ∈ Top

Proof of Theorem 0ntop
StepHypRef Expression
1 noel 4326 . 2 ¬ ∅ ∈ ∅
2 0opn 22799 . 2 (∅ ∈ Top → ∅ ∈ ∅)
31, 2mto 196 1 ¬ ∅ ∈ Top
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2099  c0 4318  Topctop 22788
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-11 2147  ax-ext 2699  ax-sep 5293
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3472  df-dif 3948  df-in 3952  df-ss 3962  df-nul 4319  df-pw 4600  df-sn 4625  df-uni 4904  df-top 22789
This theorem is referenced by:  istps  22829  ordcmp  35925  onint1  35927  kelac1  42481
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