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Theorem limuni 4425
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 4399 . 2  |-  ( Lim 
A  <->  ( Ord  A  /\  (/)  e.  A  /\  A  =  U. A ) )
21simp3bi 1016 1  |-  ( Lim 
A  ->  A  =  U. A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1364    e. wcel 2164   (/)c0 3446   U.cuni 3835   Ord word 4391   Lim wlim 4393
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 982  df-ilim 4398
This theorem is referenced by:  limuni2  4426  nlimsucg  4594  freccllem  6446  frecfcllem  6448  frecsuclem  6450
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