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Definition df-lim 4586
Description: Define the limit ordinal predicate, which is true for a non-empty ordinal that is not a successor (i.e. that is the union of itself). Our definition combines the definition of Lim of [BellMachover] p. 471 and Exercise 1 of [TakeutiZaring] p. 42. See dflim2 4637, dflim3 4827, and dflim4 for alternate definitions. (Contributed by NM, 22-Apr-1994.)
Assertion
Ref Expression
df-lim  |-  ( Lim 
A  <->  ( Ord  A  /\  A  =/=  (/)  /\  A  =  U. A ) )

Detailed syntax breakdown of Definition df-lim
StepHypRef Expression
1 cA . . 3  class  A
21wlim 4582 . 2  wff  Lim  A
31word 4580 . . 3  wff  Ord  A
4 c0 3628 . . . 4  class  (/)
51, 4wne 2599 . . 3  wff  A  =/=  (/)
61cuni 4015 . . . 4  class  U. A
71, 6wceq 1652 . . 3  wff  A  = 
U. A
83, 5, 7w3a 936 . 2  wff  ( Ord 
A  /\  A  =/=  (/) 
/\  A  =  U. A )
92, 8wb 177 1  wff  ( Lim 
A  <->  ( Ord  A  /\  A  =/=  (/)  /\  A  =  U. A ) )
Colors of variables: wff set class
This definition is referenced by:  limeq  4593  dflim2  4637  limord  4640  limuni  4641  unizlim  4698  limon  4816  dflim3  4827  nnsuc  4862  onfununi  6603  abianfplem  6715  dfrdg2  25423  ellimits  25755
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