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Theorem onordi 4262
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 4211 . 2  |-  ( A  e.  On  ->  Ord  A )
31, 2ax-mp 7 1  |-  Ord  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1439   Ord word 4198   Oncon0 4199
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2622  df-in 3006  df-ss 3013  df-uni 3660  df-tr 3943  df-iord 4202  df-on 4204
This theorem is referenced by:  ontrci  4263  onsucssi  4336  onsucsssucexmid  4356  onirri  4372
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