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Theorem onuni 4489
Description: The union of an ordinal number is an ordinal number. (Contributed by NM, 29-Sep-2006.)
Assertion
Ref Expression
onuni  |-  ( A  e.  On  ->  U. A  e.  On )

Proof of Theorem onuni
StepHypRef Expression
1 onss 4488 . 2  |-  ( A  e.  On  ->  A  C_  On )
2 ssonuni 4483 . 2  |-  ( A  e.  On  ->  ( A  C_  On  ->  U. A  e.  On ) )
31, 2mpd 13 1  |-  ( A  e.  On  ->  U. A  e.  On )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2148    C_ wss 3129   U.cuni 3807   Oncon0 4359
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-sep 4118  ax-un 4429
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-v 2739  df-in 3135  df-ss 3142  df-uni 3808  df-tr 4099  df-iord 4362  df-on 4364
This theorem is referenced by: (None)
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