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Theorem onordi 4513
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 4418 . 2  |-  ( A  e.  On  ->  Ord  A )
31, 2ax-mp 8 1  |-  Ord  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   Ord word 4407   Oncon0 4408
This theorem is referenced by:  ontrci  4514  onirri  4515  onun2i  4524  onuniorsuci  4646  onsucssi  4648  oawordeulem  6568  omopthi  6671  wfelirr  7513  bndrank  7529  rankprb  7539  rankuniss  7554  rankelun  7560  rankelpr  7561  rankelop  7562  rankxplim3  7567  rankxpsuc  7568  cardlim  7621  carduni  7630  dfac8b  7674  alephdom2  7730  alephfp  7751  dfac12lem2  7786  pm110.643ALT  7820  cfsmolem  7912  ttukeylem6  8157  ttukeylem7  8158  unsnen  8191  mreexexd  13566  efgmnvl  15039  nodenselem4  24409  hfuni  24886  pwfi2f1o  27363
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-in 3172  df-ss 3179  df-uni 3844  df-tr 4130  df-po 4330  df-so 4331  df-fr 4368  df-we 4370  df-ord 4411  df-on 4412
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