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Theorem topnem 24911
Description: A topology is not empty. (Contributed by FL, 1-Jun-2008.)
Assertion
Ref Expression
topnem  |-  ( J  e.  Top  ->  J  =/=  (/) )

Proof of Theorem topnem
StepHypRef Expression
1 0ntop 16645 . 2  |-  -.  (/)  e.  Top
2 nelne2 2537 . 2  |-  ( ( J  e.  Top  /\  -.  (/)  e.  Top )  ->  J  =/=  (/) )
31, 2mpan2 654 1  |-  ( J  e.  Top  ->  J  =/=  (/) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    e. wcel 1685    =/= wne 2447   (/)c0 3456   Topctop 16625
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867  ax-ext 2265  ax-sep 4142
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-ral 2549  df-rex 2550  df-v 2791  df-dif 3156  df-in 3160  df-ss 3167  df-nul 3457  df-pw 3628  df-sn 3647  df-uni 3829  df-top 16630
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