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Theorem limuni2 4880
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 4879 . . 3  |-  ( Lim 
A  ->  A  =  U. A )
2 limeq 4831 . . 3  |-  ( A  =  U. A  -> 
( Lim  A  <->  Lim  U. A
) )
31, 2syl 16 . 2  |-  ( Lim 
A  ->  ( Lim  A  <->  Lim  U. A ) )
43ibi 241 1  |-  ( Lim 
A  ->  Lim  U. A
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    = wceq 1370   U.cuni 4191   Lim wlim 4820
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-in 3435  df-ss 3442  df-uni 4192  df-tr 4486  df-po 4741  df-so 4742  df-fr 4779  df-we 4781  df-ord 4822  df-lim 4824
This theorem is referenced by:  rankxplim2  8190  rankxplim3  8191
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