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Theorem topnem 25512
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 16651 . 2  |-  -.  (/)  e.  Top
2 nelne2 2536 . 2  |-  ( ( J  e.  Top  /\  -.  (/)  e.  Top )  ->  J  =/=  (/) )
31, 2mpan2 652 1  |-  ( J  e.  Top  ->  J  =/=  (/) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1684    =/= wne 2446   (/)c0 3455   Topctop 16631
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-sn 3646  df-uni 3828  df-top 16636
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