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Theorem orduniss 4667
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 4587 . 2  |-  ( Ord 
A  ->  Tr  A
)
2 df-tr 4295 . 2  |-  ( Tr  A  <->  U. A  C_  A
)
31, 2sylib 189 1  |-  ( Ord 
A  ->  U. A  C_  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3312   U.cuni 4007   Tr wtr 4294   Ord word 4572
This theorem is referenced by:  orduniorsuc  4801  onfununi  6594  rankuniss  7781  r1limwun  8600  ontgval  26129
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361  df-tr 4295  df-ord 4576
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