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Theorem onordi 6476
Description: An ordinal number is an ordinal class. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
on.1 𝐴 ∈ On
Assertion
Ref Expression
onordi Ord 𝐴

Proof of Theorem onordi
StepHypRef Expression
1 on.1 . 2 𝐴 ∈ On
2 eloni 6375 . 2 (𝐴 ∈ On → Ord 𝐴)
31, 2ax-mp 5 1 Ord 𝐴
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Ord word 6364  Oncon0 6365
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3063  df-v 3477  df-in 3956  df-ss 3966  df-uni 4910  df-tr 5267  df-po 5589  df-so 5590  df-fr 5632  df-we 5634  df-ord 6368  df-on 6369
This theorem is referenced by:  onirri  6478  onsucssi  7830  ord1eln01  8496  ord2eln012  8497  oawordeulem  8554  omopthi  8660  en2  9281  en3  9282  ssttrcl  9710  ttrcltr  9711  dmttrcl  9716  ttrclselem2  9721  bndrank  9836  rankprb  9846  rankuniss  9861  rankelun  9867  rankelpr  9868  rankelop  9869  rankmapu  9873  rankxplim3  9876  rankxpsuc  9877  cardlim  9967  carduni  9976  dfac8b  10026  alephdom2  10082  alephfp  10103  dfac12lem2  10139  dju1p1e2ALT  10169  cfsmolem  10265  ttukeylem6  10509  ttukeylem7  10510  unsnen  10548  efgmnvl  19582  nogt01o  27199  scutbdaybnd2lim  27319  slerec  27321  bday1s  27333  cuteq1  27335  newbday  27397  negsproplem7  27511  mulsproplem13  27587  mulsproplem14  27588  sltonold  27690  hfuni  35187  finxpsuclem  36326  pwfi2f1o  41886
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