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Theorem 0ntop 22911
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 4338 . 2 ¬ ∅ ∈ ∅
2 0opn 22910 . 2 (∅ ∈ Top → ∅ ∈ ∅)
31, 2mto 197 1 ¬ ∅ ∈ Top
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2108  c0 4333  Topctop 22899
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-11 2157  ax-ext 2708  ax-sep 5296
This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-in 3958  df-ss 3968  df-nul 4334  df-pw 4602  df-sn 4627  df-uni 4908  df-top 22900
This theorem is referenced by:  istps  22940  ordcmp  36448  onint1  36450  kelac1  43075
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