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Definition df-ilim 4053
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 A ≠ ∅ to A (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 4054 instead for naming consistency with set.mm. (New usage is discouraged.)
Assertion
Ref Expression
df-ilim (Lim A ↔ (Ord A A A = A))

Detailed syntax breakdown of Definition df-ilim
StepHypRef Expression
1 cA . . 3 class A
21wlim 4048 . 2 wff Lim A
31word 4046 . . 3 wff Ord A
4 c0 3200 . . . 4 class
54, 1wcel 1375 . . 3 wff A
61cuni 3553 . . . 4 class A
71, 6wceq 1228 . . 3 wff A = A
83, 5, 7w3a 873 . 2 wff (Ord A A A = A)
92, 8wb 98 1 wff (Lim A ↔ (Ord A A A = A))
Colors of variables: wff set class
This definition is referenced by:  dflim2  4054
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