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Theorem epweon 4512
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 4511 . 2  |-  Ord  On
2 ordwe 4342 . 2  |-  ( Ord 
On  ->  _E  We  On )
31, 2ax-mp 10 1  |-  _E  We  On
Colors of variables: wff set class
Syntax hints:    _E cep 4240    We wwe 4288   Ord word 4328   Oncon0 4329
This theorem is referenced by:  onnseq  6294  ordunifi  7040  ordtypelem8  7173  oismo  7188  cantnfcl  7301  leweon  7572  r0weon  7573  ac10ct  7594  dfac12lem2  7703  cflim2  7822  cofsmo  7828  hsmexlem1  7985  smobeth  8141  gruina  8373  ltsopi  8445  omsinds  23553  tfrALTlem  23610  tfr1ALT  23611  tfr2ALT  23612  tfr3ALT  23613  finminlem  25563  dnwech  26477  aomclem4  26486
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-13 1625  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237  ax-sep 4081  ax-nul 4089  ax-pr 4152  ax-un 4449
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 940  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2121  df-mo 2122  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-ral 2520  df-rex 2521  df-rab 2523  df-v 2742  df-sbc 2936  df-dif 3097  df-un 3099  df-in 3101  df-ss 3108  df-pss 3110  df-nul 3398  df-if 3507  df-sn 3587  df-pr 3588  df-tp 3589  df-op 3590  df-uni 3769  df-br 3964  df-opab 4018  df-tr 4054  df-eprel 4242  df-po 4251  df-so 4252  df-fr 4289  df-we 4291  df-ord 4332  df-on 4333
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