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Theorem orduniss 4711
Description: An ordinal class includes its union. (Contributed by NM, 13-Sep-2003.)
Assertion
Ref Expression
orduniss  |-  ( Ord 
A  ->  U. A  C_  A )

Proof of Theorem orduniss
StepHypRef Expression
1 ordtr 4630 . 2  |-  ( Ord 
A  ->  Tr  A
)
2 df-tr 4334 . 2  |-  ( Tr  A  <->  U. A  C_  A
)
31, 2sylib 190 1  |-  ( Ord 
A  ->  U. A  C_  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3309   U.cuni 4044   Tr wtr 4333   Ord word 4615
This theorem is referenced by:  orduniorsuc  4845  onfununi  6639  rankuniss  7828  r1limwun  8649  ontgval  26216
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 179  df-an 362  df-tr 4334  df-ord 4619
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