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

Theorem orduni 4274
Description: The union of an ordinal class is ordinal. (Contributed by NM, 12-Sep-2003.)
Assertion
Ref Expression
orduni (Ord 𝐴 → Ord 𝐴)

Proof of Theorem orduni
StepHypRef Expression
1 ordsson 4271 . 2 (Ord 𝐴𝐴 ⊆ On)
2 ssorduni 4266 . 2 (𝐴 ⊆ On → Ord 𝐴)
31, 2syl 14 1 (Ord 𝐴 → Ord 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2984   cuni 3627  Ord word 4152  Oncon0 4153
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-3an 922  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 2614  df-in 2990  df-ss 2997  df-uni 3628  df-tr 3902  df-iord 4156  df-on 4158
This theorem is referenced by:  tfrcl  6060
  Copyright terms: Public domain W3C validator