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Theorem orduniss 5819
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 5735 . 2 (Ord 𝐴 → Tr 𝐴)
2 df-tr 4751 . 2 (Tr 𝐴 𝐴𝐴)
31, 2sylib 208 1 (Ord 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3572   cuni 4434  Tr wtr 4750  Ord word 5720
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 197  df-an 386  df-tr 4751  df-ord 5724
This theorem is referenced by:  orduniorsuc  7027  onfununi  7435  rankuniss  8726  r1limwun  9555  ontgval  32414
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