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Theorem limuni 4180
Description: A limit ordinal is its own supremum (union). (Contributed by NM, 4-May-1995.)
Assertion
Ref Expression
limuni  |-  ( Lim 
A  ->  A  =  U. A )

Proof of Theorem limuni
StepHypRef Expression
1 dflim2 4154 . 2  |-  ( Lim 
A  <->  ( Ord  A  /\  (/)  e.  A  /\  A  =  U. A ) )
21simp3bi 956 1  |-  ( Lim 
A  ->  A  =  U. A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285    e. wcel 1434   (/)c0 3268   U.cuni 3622   Ord word 4146   Lim wlim 4148
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922  df-ilim 4153
This theorem is referenced by:  limuni2  4181  nlimsucg  4338  freccllem  6072  frecfcllem  6074  frecsuclem  6076
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