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Theorem orduniss 4190
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 4143 . 2  |-  ( Ord 
A  ->  Tr  A
)
2 df-tr 3883 . 2  |-  ( Tr  A  <->  U. A  C_  A
)
31, 2sylib 131 1  |-  ( Ord 
A  ->  U. A  C_  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 2945   U.cuni 3608   Tr wtr 3882   Ord word 4127
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103
This theorem depends on definitions:  df-bi 114  df-tr 3883  df-iord 4131
This theorem is referenced by:  ordunisuc2r  4268  limom  4364
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