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Theorem topnem 25523
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 16653 . 2  |-  -.  (/)  e.  Top
2 nelne2 2538 . 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 1686    =/= wne 2448   (/)c0 3457   Topctop 16633
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266  ax-sep 4143
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ne 2450  df-ral 2550  df-rex 2551  df-v 2792  df-dif 3157  df-in 3161  df-ss 3168  df-nul 3458  df-pw 3629  df-sn 3648  df-uni 3830  df-top 16638
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