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Theorem epweon 6945
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 6944 . 2 Ord On
2 ordwe 5705 . 2 (Ord On → E We On)
31, 2ax-mp 5 1 E We On
Colors of variables: wff setvar class
Syntax hints:   E cep 4993   We wwe 5042  Ord word 5691  Oncon0 5692
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-8 1989  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4751  ax-nul 4759  ax-pr 4877  ax-un 6914
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1037  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-mo 2474  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ne 2791  df-ral 2913  df-rex 2914  df-rab 2917  df-v 3192  df-sbc 3423  df-dif 3563  df-un 3565  df-in 3567  df-ss 3574  df-pss 3576  df-nul 3898  df-if 4065  df-sn 4156  df-pr 4158  df-tp 4160  df-op 4162  df-uni 4410  df-br 4624  df-opab 4684  df-tr 4723  df-eprel 4995  df-po 5005  df-so 5006  df-fr 5043  df-we 5045  df-ord 5695  df-on 5696
This theorem is referenced by:  omsinds  7046  onnseq  7401  dfrecs3  7429  tfr1ALT  7456  tfr2ALT  7457  tfr3ALT  7458  ordunifi  8170  ordtypelem8  8390  oismo  8405  cantnfcl  8524  leweon  8794  r0weon  8795  ac10ct  8817  dfac12lem2  8926  cflim2  9045  cofsmo  9051  hsmexlem1  9208  smobeth  9368  gruina  9600  ltsopi  9670  dford5  31370  finminlem  32007  dnwech  37137  aomclem4  37146
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