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Theorem orduni 4421
 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 4418 . 2 (Ord 𝐴𝐴 ⊆ On)
2 ssorduni 4413 . 2 (𝐴 ⊆ On → Ord 𝐴)
31, 2syl 14 1 (Ord 𝐴 → Ord 𝐴)
 Colors of variables: wff set class Syntax hints:   → wi 4   ⊆ wss 3077  ∪ cuni 3745  Ord word 4294  Oncon0 4295 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2692  df-in 3083  df-ss 3090  df-uni 3746  df-tr 4036  df-iord 4298  df-on 4300 This theorem is referenced by:  tfrcl  6272
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