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Theorem epweon 6393
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 6392 . 2  |-  Ord  On
2 ordwe 4730 . 2  |-  ( Ord 
On  ->  _E  We  On )
31, 2ax-mp 5 1  |-  _E  We  On
Colors of variables: wff setvar class
Syntax hints:    _E cep 4628    We wwe 4676   Ord word 4716   Oncon0 4717
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-8 1758  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2422  ax-sep 4411  ax-nul 4419  ax-pr 4529  ax-un 6370
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 966  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2257  df-mo 2258  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-ne 2606  df-ral 2718  df-rex 2719  df-rab 2722  df-v 2972  df-sbc 3185  df-dif 3329  df-un 3331  df-in 3333  df-ss 3340  df-pss 3342  df-nul 3636  df-if 3790  df-sn 3876  df-pr 3878  df-tp 3880  df-op 3882  df-uni 4090  df-br 4291  df-opab 4349  df-tr 4384  df-eprel 4630  df-po 4639  df-so 4640  df-fr 4677  df-we 4679  df-ord 4720  df-on 4721
This theorem is referenced by:  onnseq  6803  ordunifi  7560  ordtypelem8  7737  oismo  7752  cantnfcl  7873  cantnfclOLD  7903  leweon  8176  r0weon  8177  ac10ct  8202  dfac12lem2  8311  cflim2  8430  cofsmo  8436  hsmexlem1  8593  smobeth  8748  gruina  8983  ltsopi  9055  omsinds  27678  tfrALTlem  27741  tfr1ALT  27742  tfr2ALT  27743  tfr3ALT  27744  finminlem  28510  dnwech  29398  aomclem4  29407
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