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Theorem onordi 4925
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 4831 . 2  |-  ( A  e.  On  ->  Ord  A )
31, 2ax-mp 5 1  |-  Ord  A
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1842   Ord word 4820   Oncon0 4821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-rex 2759  df-v 3060  df-in 3420  df-ss 3427  df-uni 4191  df-tr 4489  df-po 4743  df-so 4744  df-fr 4781  df-we 4783  df-ord 4824  df-on 4825
This theorem is referenced by:  ontrci  4926  onirri  4927  onun2i  4936  onuniorsuci  6612  onsucssi  6614  oawordeulem  7160  omopthi  7263  bndrank  8211  rankprb  8221  rankuniss  8236  rankelun  8242  rankelpr  8243  rankelop  8244  rankmapu  8248  rankxplim3  8251  rankxpsuc  8252  cardlim  8305  carduni  8314  dfac8b  8364  alephdom2  8420  alephfp  8441  dfac12lem2  8476  pm110.643ALT  8510  cfsmolem  8602  ttukeylem6  8846  ttukeylem7  8847  unsnen  8880  mreexexd  15154  efgmnvl  16948  nodenselem4  30117  hfuni  30510  pwfi2f1o  35387  pwfi2f1oOLD  35388
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