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Theorem epweon 4723
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 4722 . 2  |-  Ord  On
2 ordwe 4554 . 2  |-  ( Ord 
On  ->  _E  We  On )
31, 2ax-mp 8 1  |-  _E  We  On
Colors of variables: wff set class
Syntax hints:    _E cep 4452    We wwe 4500   Ord word 4540   Oncon0 4541
This theorem is referenced by:  onnseq  6565  ordunifi  7316  ordtypelem8  7450  oismo  7465  cantnfcl  7578  leweon  7849  r0weon  7850  ac10ct  7871  dfac12lem2  7980  cflim2  8099  cofsmo  8105  hsmexlem1  8262  smobeth  8417  gruina  8649  ltsopi  8721  omsinds  25433  tfrALTlem  25490  tfr1ALT  25491  tfr2ALT  25492  tfr3ALT  25493  finminlem  26211  dnwech  27013  aomclem4  27022
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pr 4363  ax-un 4660
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-sbc 3122  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-pss 3296  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-tp 3782  df-op 3783  df-uni 3976  df-br 4173  df-opab 4227  df-tr 4263  df-eprel 4454  df-po 4463  df-so 4464  df-fr 4501  df-we 4503  df-ord 4544  df-on 4545
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