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Theorem 0ntop 21520
 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 4247 . 2 ¬ ∅ ∈ ∅
2 0opn 21519 . 2 (∅ ∈ Top → ∅ ∈ ∅)
31, 2mto 200 1 ¬ ∅ ∈ Top
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∈ wcel 2111  ∅c0 4243  Topctop 21508 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5168 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rex 3112  df-rab 3115  df-v 3443  df-dif 3884  df-in 3888  df-ss 3898  df-nul 4244  df-pw 4499  df-sn 4526  df-uni 4802  df-top 21509 This theorem is referenced by:  istps  21549  ordcmp  33923  onint1  33925  kelac1  40050
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