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Theorem orduni 4512
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 4509 . 2 (Ord 𝐴𝐴 ⊆ On)
2 ssorduni 4504 . 2 (𝐴 ⊆ On → Ord 𝐴)
31, 2syl 14 1 (Ord 𝐴 → Ord 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 3144   cuni 3824  Ord word 4380  Oncon0 4381
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2754  df-in 3150  df-ss 3157  df-uni 3825  df-tr 4117  df-iord 4384  df-on 4386
This theorem is referenced by:  tfrcl  6390
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