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Theorem onuni 4220
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 4219 . 2  |-  ( A  e.  On  ->  A  C_  On )
2 ssonuni 4214 . 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 1393    C_ wss 2917   U.cuni 3580   Oncon0 4100
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-un 4170
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-uni 3581  df-tr 3855  df-iord 4103  df-on 4105
This theorem is referenced by: (None)
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