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	|- ( Lim A <-> ( Ord A /\ A =/= (/) /\ A = U. A ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	|- A
1	0	wlim	|- Lim A
2	0	word	|- Ord A
3		c0	|- (/)
4	0 3	wne	|- A =/= (/)
5	0	cuni	|- U. A
6	0 5	wceq	|- A = U. A
7	2 4 6	w3a	|- ( Ord A /\ A =/= (/) /\ A = U. A )
8	1 7	wb	|- ( Lim A <-> ( Ord A /\ A =/= (/) /\ A = U. A ) )