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Theorem epweon 4577
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 4576 . 2  |-  Ord  On
2 ordwe 4407 . 2  |-  ( Ord 
On  ->  _E  We  On )
31, 2ax-mp 8 1  |-  _E  We  On
Colors of variables: wff set class
Syntax hints:    _E cep 4305    We wwe 4353   Ord word 4393   Oncon0 4394
This theorem is referenced by:  onnseq  6363  ordunifi  7109  ordtypelem8  7242  oismo  7257  cantnfcl  7370  leweon  7641  r0weon  7642  ac10ct  7663  dfac12lem2  7772  cflim2  7891  cofsmo  7897  hsmexlem1  8054  smobeth  8210  gruina  8442  ltsopi  8514  omsinds  24221  tfrALTlem  24278  tfr1ALT  24279  tfr2ALT  24280  tfr3ALT  24281  finminlem  26242  dnwech  27156  aomclem4  27165
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-13 1688  ax-14 1690  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266  ax-sep 4143  ax-nul 4151  ax-pr 4216  ax-un 4514
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 1531  df-nf 1534  df-sb 1632  df-eu 2149  df-mo 2150  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ne 2450  df-ral 2550  df-rex 2551  df-rab 2554  df-v 2792  df-sbc 2994  df-dif 3157  df-un 3159  df-in 3161  df-ss 3168  df-pss 3170  df-nul 3458  df-if 3568  df-sn 3648  df-pr 3649  df-tp 3650  df-op 3651  df-uni 3830  df-br 4026  df-opab 4080  df-tr 4116  df-eprel 4307  df-po 4316  df-so 4317  df-fr 4354  df-we 4356  df-ord 4397  df-on 4398
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