Metamath Proof Explorer


Definition df-lim

Description: Define the limit ordinal predicate, which is true for a nonempty 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 , dflim3 , and dflim4 for alternate definitions. (Contributed by NM, 22-Apr-1994)

Ref Expression
Assertion df-lim LimAOrdAAA=A

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA classA
1 0 wlim wffLimA
2 0 word wffOrdA
3 c0 class
4 0 3 wne wffA
5 0 cuni classA
6 0 5 wceq wffA=A
7 2 4 6 w3a wffOrdAAA=A
8 1 7 wb wffLimAOrdAAA=A