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Theorem orduni 4221
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 4218 . 2 (Ord 𝐴𝐴 ⊆ On)
2 ssorduni 4213 . 2 (𝐴 ⊆ On → Ord 𝐴)
31, 2syl 14 1 (Ord 𝐴 → Ord 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2917   cuni 3580  Ord word 4099  Oncon0 4100
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-uni 3581  df-tr 3855  df-iord 4103  df-on 4105
This theorem is referenced by: (None)
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