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Theorem epweon 4575
Description: The epsilon relation well-orders the class of ordinal numbers. Proposition 4.8(g) of [Mendelson] p. 244. (Contributed by NM, 1-Nov-2003.)
Assertion
Ref Expression
epweon  |-  _E  We  On

Proof of Theorem epweon
StepHypRef Expression
1 ordon 4574 . 2  |-  Ord  On
2 ordwe 4405 . 2  |-  ( Ord 
On  ->  _E  We  On )
31, 2ax-mp 8 1  |-  _E  We  On
Colors of variables: wff set class
Syntax hints:    _E cep 4303    We wwe 4351   Ord word 4391   Oncon0 4392
This theorem is referenced by:  onnseq  6361  ordunifi  7107  ordtypelem8  7240  oismo  7255  cantnfcl  7368  leweon  7639  r0weon  7640  ac10ct  7661  dfac12lem2  7770  cflim2  7889  cofsmo  7895  hsmexlem1  8052  smobeth  8208  gruina  8440  ltsopi  8512  omsinds  24219  tfrALTlem  24276  tfr1ALT  24277  tfr2ALT  24278  tfr3ALT  24279  finminlem  26231  dnwech  27145  aomclem4  27154
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-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-un 4512
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-pss 3168  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-tp 3648  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-tr 4114  df-eprel 4305  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395  df-on 4396
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