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Theorem epweon 4574
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 4573 . 2  |-  Ord  On
2 ordwe 4404 . 2  |-  ( Ord 
On  ->  _E  We  On )
31, 2ax-mp 8 1  |-  _E  We  On
Colors of variables: wff set class
Syntax hints:    _E cep 4302    We wwe 4350   Ord word 4390   Oncon0 4391
This theorem is referenced by:  onnseq  6357  ordunifi  7103  ordtypelem8  7236  oismo  7251  cantnfcl  7364  leweon  7635  r0weon  7636  ac10ct  7657  dfac12lem2  7766  cflim2  7885  cofsmo  7891  hsmexlem1  8048  smobeth  8204  gruina  8436  ltsopi  8508  omsinds  23623  tfrALTlem  23680  tfr1ALT  23681  tfr2ALT  23682  tfr3ALT  23683  finminlem  25642  dnwech  26556  aomclem4  26565
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 1636  ax-8 1644  ax-13 1687  ax-14 1689  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2265  ax-sep 4142  ax-nul 4150  ax-pr 4213  ax-un 4511
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 1631  df-eu 2148  df-mo 2149  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-ral 2549  df-rex 2550  df-rab 2553  df-v 2791  df-sbc 2993  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-pss 3169  df-nul 3457  df-if 3567  df-sn 3647  df-pr 3648  df-tp 3649  df-op 3650  df-uni 3829  df-br 4025  df-opab 4079  df-tr 4115  df-eprel 4304  df-po 4313  df-so 4314  df-fr 4351  df-we 4353  df-ord 4394  df-on 4395
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