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Theorem limuni2 4180
Description: The union of a limit ordinal is a limit ordinal. (Contributed by NM, 19-Sep-2006.)
Assertion
Ref Expression
limuni2  |-  ( Lim 
A  ->  Lim  U. A
)

Proof of Theorem limuni2
StepHypRef Expression
1 limuni 4179 . . 3  |-  ( Lim 
A  ->  A  =  U. A )
2 limeq 4160 . . 3  |-  ( A  =  U. A  -> 
( Lim  A  <->  Lim  U. A
) )
31, 2syl 14 . 2  |-  ( Lim 
A  ->  ( Lim  A  <->  Lim  U. A ) )
43ibi 174 1  |-  ( Lim 
A  ->  Lim  U. A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    = wceq 1285   U.cuni 3621   Lim wlim 4147
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-in 2988  df-ss 2995  df-uni 3622  df-tr 3896  df-iord 4149  df-ilim 4152
This theorem is referenced by: (None)
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