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Theorem 0ntop 20758
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 3952 . 2 ¬ ∅ ∈ ∅
2 0opn 20757 . 2 (∅ ∈ Top → ∅ ∈ ∅)
31, 2mto 188 1 ¬ ∅ ∈ Top
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2030  c0 3948  Topctop 20746
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rex 2947  df-v 3233  df-dif 3610  df-in 3614  df-ss 3621  df-nul 3949  df-pw 4193  df-sn 4211  df-uni 4469  df-top 20747
This theorem is referenced by:  istps  20786  ordcmp  32571  onint1  32573  kelac1  37950
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