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Theorem limuni 4634
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 df-lim 4579 . 2  |-  ( Lim 
A  <->  ( Ord  A  /\  A  =/=  (/)  /\  A  =  U. A ) )
21simp3bi 974 1  |-  ( Lim 
A  ->  A  =  U. A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    =/= wne 2599   (/)c0 3621   U.cuni 4008   Ord word 4573   Lim wlim 4575
This theorem is referenced by:  limuni2  4635  unizlim  4691  nlimsucg  4815  oa0r  6775  om1r  6779  oarec  6798  oeworde  6829  oeeulem  6837  infeq5i  7584  r1sdom  7693  rankxplim3  7798  cflm  8123  coflim  8134  cflim2  8136  cfss  8138  cfslbn  8140  limsucncmpi  26188
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-lim 4579
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