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Theorem elong 4891
Description: An ordinal number is an ordinal set. (Contributed by NM, 5-Jun-1994.)
Assertion
Ref Expression
elong

Proof of Theorem elong
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ordeq 4890 . 2
2 df-on 4887 . 2
31, 2elab2g 3248 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  e.wcel 1818  Ordword 4882   con0 4883
This theorem is referenced by:  elon  4892  eloni  4893  elon2  4894  ordelon  4907  onin  4914  limelon  4946  ordsssuc2  4971  onprc  6620  ssonuni  6622  suceloni  6648  ordsuc  6649  oion  7982  hartogs  7990  card2on  8001  tskwe  8352  onssnum  8442  hsmexlem1  8827  ondomon  8959  1stcrestlem  19953  hfninf  29843
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887
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