ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  onordi GIF version

Theorem onordi 4209
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 4158 . 2 (𝐴 ∈ On → Ord 𝐴)
31, 2ax-mp 7 1 Ord 𝐴
Colors of variables: wff set class
Syntax hints:  wcel 1434  Ord word 4145  Oncon0 4146
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-in 2988  df-ss 2995  df-uni 3622  df-tr 3896  df-iord 4149  df-on 4151
This theorem is referenced by:  ontrci  4210  onsucssi  4278  onsucsssucexmid  4298  onirri  4314
  Copyright terms: Public domain W3C validator