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

Theorem orduni 4187
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 4184 . 2 (Ord AA ⊆ On)
2 ssorduni 4179 . 2 (A ⊆ On → Ord A)
31, 2syl 14 1 (Ord A → Ord A)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2911   cuni 3571  Ord word 4065  Oncon0 4066
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-in 2918  df-ss 2925  df-uni 3572  df-tr 3846  df-iord 4069  df-on 4071
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator