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Theorem onordi 4316
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 4265 . 2 (𝐴 ∈ On → Ord 𝐴)
31, 2ax-mp 5 1 Ord 𝐴
Colors of variables: wff set class
Syntax hints:  wcel 1463  Ord word 4252  Oncon0 4253
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rex 2397  df-v 2660  df-in 3045  df-ss 3052  df-uni 3705  df-tr 3995  df-iord 4256  df-on 4258
This theorem is referenced by:  ontrci  4317  onsucssi  4390  onsucsssucexmid  4410  onirri  4426
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