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Theorem 0ntop 16980
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 3634 . 2  |-  -.  (/)  e.  (/)
2 0opn 16979 . 2  |-  ( (/)  e.  Top  ->  (/)  e.  (/) )
31, 2mto 170 1  |-  -.  (/)  e.  Top
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1726   (/)c0 3630   Topctop 16960
This theorem is referenced by:  istps  17003  ordcmp  26199  onint1  26201  kelac1  27140
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-nul 3631  df-pw 3803  df-sn 3822  df-uni 4018  df-top 16965
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