MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tsk0 Unicode version

Theorem tsk0 9162
Description: A nonempty Tarski 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 3794 . . 3
2 0ss 3814 . . . . . 6
3 tskss 9157 . . . . . 6
42, 3mp3an3 1313 . . . . 5
54expcom 435 . . . 4
65exlimiv 1722 . . 3
71, 6sylbi 195 . 2
87impcom 430 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  E.wex 1612  e.wcel 1818  =/=wne 2652  C_wss 3475   c0 3784   ctsk 9147
This theorem is referenced by:  tsk1  9163  tskr1om  9166
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-pw 4014  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-tsk 9148
  Copyright terms: Public domain W3C validator