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Theorem onordi 4678
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 4583 . 2  |-  ( A  e.  On  ->  Ord  A )
31, 2ax-mp 8 1  |-  Ord  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   Ord word 4572   Oncon0 4573
This theorem is referenced by:  ontrci  4679  onirri  4680  onun2i  4689  onuniorsuci  4811  onsucssi  4813  oawordeulem  6789  omopthi  6892  bndrank  7759  rankprb  7769  rankuniss  7784  rankelun  7790  rankelpr  7791  rankelop  7792  rankxplim3  7797  rankxpsuc  7798  cardlim  7851  carduni  7860  dfac8b  7904  alephdom2  7960  alephfp  7981  dfac12lem2  8016  pm110.643ALT  8050  cfsmolem  8142  ttukeylem6  8386  ttukeylem7  8387  unsnen  8420  mreexexd  13865  efgmnvl  15338  nodenselem4  25631  hfuni  26117  pwfi2f1o  27218
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-in 3319  df-ss 3326  df-uni 4008  df-tr 4295  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577
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