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Theorem epweon 4678
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 4677 . 2  |-  Ord  On
2 ordwe 4508 . 2  |-  ( Ord 
On  ->  _E  We  On )
31, 2ax-mp 8 1  |-  _E  We  On
Colors of variables: wff set class
Syntax hints:    _E cep 4406    We wwe 4454   Ord word 4494   Oncon0 4495
This theorem is referenced by:  onnseq  6503  ordunifi  7254  ordtypelem8  7387  oismo  7402  cantnfcl  7515  leweon  7786  r0weon  7787  ac10ct  7808  dfac12lem2  7917  cflim2  8036  cofsmo  8042  hsmexlem1  8199  smobeth  8355  gruina  8587  ltsopi  8659  omsinds  24960  tfrALTlem  25017  tfr1ALT  25018  tfr2ALT  25019  tfr3ALT  25020  finminlem  25738  dnwech  26651  aomclem4  26660
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-13 1717  ax-14 1719  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347  ax-sep 4243  ax-nul 4251  ax-pr 4316  ax-un 4615
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 936  df-3an 937  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-eu 2221  df-mo 2222  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-ne 2531  df-ral 2633  df-rex 2634  df-rab 2637  df-v 2875  df-sbc 3078  df-dif 3241  df-un 3243  df-in 3245  df-ss 3252  df-pss 3254  df-nul 3544  df-if 3655  df-sn 3735  df-pr 3736  df-tp 3737  df-op 3738  df-uni 3930  df-br 4126  df-opab 4180  df-tr 4216  df-eprel 4408  df-po 4417  df-so 4418  df-fr 4455  df-we 4457  df-ord 4498  df-on 4499
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