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Theorem tsk0 8639
 Description: A non-empty Tarski's class contains the empty set. (Contributed by FL, 30-Dec-2010.) (Revised by Mario Carneiro, 18-Jun-2013.)
Assertion
Ref Expression
tsk0

Proof of Theorem tsk0
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 n0 3638 . . 3
2 0ss 3657 . . . . . 6
3 tskss 8634 . . . . . 6
42, 3mp3an3 1269 . . . . 5
54expcom 426 . . . 4
65exlimiv 1645 . . 3
71, 6sylbi 189 . 2
87impcom 421 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wex 1551   wcel 1726   wne 2600   wss 3321  c0 3629  ctsk 8624 This theorem is referenced by:  tsk1  8640  tskr1om  8643 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 2418  ax-sep 4331 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-pw 3802  df-sn 3821  df-pr 3822  df-op 3824  df-br 4214  df-tsk 8625
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