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Theorem 0ntop 19178
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 3789 . 2  |-  -.  (/)  e.  (/)
2 0opn 19177 . 2  |-  ( (/)  e.  Top  ->  (/)  e.  (/) )
31, 2mto 176 1  |-  -.  (/)  e.  Top
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    e. wcel 1767   (/)c0 3785   Topctop 19158
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-v 3115  df-dif 3479  df-in 3483  df-ss 3490  df-nul 3786  df-pw 4012  df-sn 4028  df-uni 4246  df-top 19163
This theorem is referenced by:  istps  19201  ordcmp  29486  onint1  29488  kelac1  30613
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