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Theorem onordi 4497
Description: An ordinal number is an ordinal class. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
on.1  |-  A  e.  On
Assertion
Ref Expression
onordi  |-  Ord  A

Proof of Theorem onordi
StepHypRef Expression
1 on.1 . 2  |-  A  e.  On
2 eloni 4402 . 2  |-  ( A  e.  On  ->  Ord  A )
31, 2ax-mp 8 1  |-  Ord  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   Ord word 4391   Oncon0 4392
This theorem is referenced by:  ontrci  4498  onirri  4499  onun2i  4508  onuniorsuci  4630  onsucssi  4632  oawordeulem  6552  omopthi  6655  wfelirr  7497  bndrank  7513  rankprb  7523  rankuniss  7538  rankelun  7544  rankelpr  7545  rankelop  7546  rankxplim3  7551  rankxpsuc  7552  cardlim  7605  carduni  7614  dfac8b  7658  alephdom2  7714  alephfp  7735  dfac12lem2  7770  pm110.643ALT  7804  cfsmolem  7896  ttukeylem6  8141  ttukeylem7  8142  unsnen  8175  mreexexd  13550  efgmnvl  15023  nodenselem4  24338  hfuni  24814  pwfi2f1o  27260
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 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-v 2790  df-in 3159  df-ss 3166  df-uni 3828  df-tr 4114  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395  df-on 4396
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