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Theorem limuni2 4453
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 4452 . . 3  |-  ( Lim 
A  ->  A  =  U. A )
2 limeq 4404 . . 3  |-  ( A  =  U. A  -> 
( Lim  A  <->  Lim  U. A
) )
31, 2syl 15 . 2  |-  ( Lim 
A  ->  ( Lim  A  <->  Lim  U. A ) )
43ibi 232 1  |-  ( Lim 
A  ->  Lim  U. A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1623   U.cuni 3827   Lim wlim 4393
This theorem is referenced by:  rankxplim2  7550  rankxplim3  7551
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-in 3159  df-ss 3166  df-uni 3828  df-tr 4114  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395  df-lim 4397
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