ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  limuni2 Unicode version

Theorem limuni2 4323
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 4322 . . 3  |-  ( Lim 
A  ->  A  =  U. A )
2 limeq 4303 . . 3  |-  ( A  =  U. A  -> 
( Lim  A  <->  Lim  U. A
) )
31, 2syl 14 . 2  |-  ( Lim 
A  ->  ( Lim  A  <->  Lim  U. A ) )
43ibi 175 1  |-  ( Lim 
A  ->  Lim  U. A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    = wceq 1332   U.cuni 3740   Lim wlim 4290
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-in 3078  df-ss 3085  df-uni 3741  df-tr 4031  df-iord 4292  df-ilim 4295
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator