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Theorem limuni2 4642
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 4641 . . 3  |-  ( Lim 
A  ->  A  =  U. A )
2 limeq 4593 . . 3  |-  ( A  =  U. A  -> 
( Lim  A  <->  Lim  U. A
) )
31, 2syl 16 . 2  |-  ( Lim 
A  ->  ( Lim  A  <->  Lim  U. A ) )
43ibi 233 1  |-  ( Lim 
A  ->  Lim  U. A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    = wceq 1652   U.cuni 4015   Lim wlim 4582
This theorem is referenced by:  rankxplim2  7804  rankxplim3  7805
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-in 3327  df-ss 3334  df-uni 4016  df-tr 4303  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584  df-lim 4586
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