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Theorem orduniss 6459
Description: An ordinal class includes its union. (Contributed by NM, 13-Sep-2003.)
Assertion
Ref Expression
orduniss (Ord 𝐴 𝐴𝐴)

Proof of Theorem orduniss
StepHypRef Expression
1 ordtr 6376 . 2 (Ord 𝐴 → Tr 𝐴)
2 df-tr 5266 . 2 (Tr 𝐴 𝐴𝐴)
31, 2sylib 217 1 (Ord 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3948   cuni 4908  Tr wtr 5265  Ord word 6361
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-an 398  df-tr 5266  df-ord 6365
This theorem is referenced by:  orduniorsuc  7815  onfununi  8338  rankuniss  9858  r1limwun  10728  ontgval  35305  onsupneqmaxlim0  41959  onsupnmax  41963
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