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Definition df-ilim 4055
Description: Define the limit ordinal predicate, which is true for an ordinal that has the empty set as an element and 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, and then changes  =/=  (/) to  (/) (which would be equivalent given the law of the excluded middle, but which is not for us). (Contributed by Jim Kingdon, 11-Nov-2018.) Use its alias dflim2 4056 instead for naming consistency with set.mm. (New usage is discouraged.)
Assertion
Ref Expression
df-ilim  Lim  Ord  (/)  U.

Detailed syntax breakdown of Definition df-ilim
StepHypRef Expression
1 cA . . 3
21wlim 4050 . 2  Lim
31word 4048 . . 3  Ord
4 c0 3201 . . . 4  (/)
54, 1wcel 1374 . . 3  (/)
61cuni 3554 . . . 4  U.
71, 6wceq 1228 . . 3  U.
83, 5, 7w3a 873 . 2  Ord  (/)  U.
92, 8wb 98 1  Lim  Ord  (/)  U.
Colors of variables: wff set class
This definition is referenced by:  dflim2  4056
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