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Theorem 0ntop 20833
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 4027 . 2 ¬ ∅ ∈ ∅
2 0opn 20832 . 2 (∅ ∈ Top → ∅ ∈ ∅)
31, 2mto 188 1 ¬ ∅ ∈ Top
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2103  c0 4023  Topctop 20821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704  ax-sep 4889
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-ral 3019  df-rex 3020  df-v 3306  df-dif 3683  df-in 3687  df-ss 3694  df-nul 4024  df-pw 4268  df-sn 4286  df-uni 4545  df-top 20822
This theorem is referenced by:  istps  20861  ordcmp  32673  onint1  32675  kelac1  38052
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