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Theorem onirri 4989
 Description: An ordinal number is not a member of itself. Theorem 7M(c) of [Enderton] p. 192. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
on.1
Assertion
Ref Expression
onirri

Proof of Theorem onirri
StepHypRef Expression
1 on.1 . . 3
21onordi 4987 . 2
3 ordirr 4901 . 2
42, 3ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  e.wcel 1818  Ordword 4882   con0 4883 This theorem is referenced by:  onssnel2i  4993  onuninsuci  6675  oelim2  7263  omopthlem2  7324  harndom  8011  wfelirr  8264  carduni  8383  pm54.43  8402  alephle  8490  alephfp  8510  pwxpndom2  9064  fvnobday  29442  onsucsuccmpi  29908  onint1  29914  wepwsolem  30987 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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 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-eu 2286  df-mo 2287  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-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-tr 4546  df-eprel 4796  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887
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