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Theorem 0ntop 12183
Description: The empty set is not a topology. (Contributed by FL, 1-Jun-2008.)
Assertion
Ref Expression
0ntop  |-  -.  (/)  e.  Top

Proof of Theorem 0ntop
StepHypRef Expression
1 noel 3367 . 2  |-  -.  (/)  e.  (/)
2 0opn 12182 . 2  |-  ( (/)  e.  Top  ->  (/)  e.  (/) )
31, 2mto 651 1  |-  -.  (/)  e.  Top
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1480   (/)c0 3363   Topctop 12173
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-dif 3073  df-in 3077  df-ss 3084  df-nul 3364  df-pw 3512  df-sn 3533  df-uni 3737  df-top 12174
This theorem is referenced by: (None)
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