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Theorem 0ntop 11956
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 3314 . 2 ¬ ∅ ∈ ∅
2 0opn 11955 . 2 (∅ ∈ Top → ∅ ∈ ∅)
31, 2mto 629 1 ¬ ∅ ∈ Top
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 1448  c0 3310  Topctop 11946
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-sep 3986
This theorem depends on definitions:  df-bi 116  df-tru 1302  df-fal 1305  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ral 2380  df-rex 2381  df-v 2643  df-dif 3023  df-in 3027  df-ss 3034  df-nul 3311  df-pw 3459  df-sn 3480  df-uni 3684  df-top 11947
This theorem is referenced by: (None)
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