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Theorem onuni 4507
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 4506 . 2  |-  ( A  e.  On  ->  A  C_  On )
2 ssonuni 4501 . 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 2159    C_ wss 3143   U.cuni 3823   Oncon0 4377
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 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-13 2161  ax-14 2162  ax-ext 2170  ax-sep 4135  ax-un 4447
This theorem depends on definitions:  df-bi 117  df-3an 981  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-nfc 2320  df-ral 2472  df-rex 2473  df-v 2753  df-in 3149  df-ss 3156  df-uni 3824  df-tr 4116  df-iord 4380  df-on 4382
This theorem is referenced by: (None)
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