Definition df-ord 4868

Description: Define the ordinal predicate, which is true for a class that is transitive and is well-ordered by the epsilon relation. Variant of definition of [BellMachover] p. 468. (Contributed by NM, 17-Sep-1993.)

Assertion

Ref	Expression
df-ord	|- ( Ord A <-> ( Tr A /\ _E We A ) )

Detailed syntax breakdown of Definition df-ord

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	word 4864	. 2 wff Ord A
3	1	wtr 4527	. . 3 wff Tr A
4		cep 4776	. . . 4 class _E
5	1, 4	wwe 4824	. . 3 wff _E We A
6	3, 5	wa 369	. 2 wff ( Tr A /\ _E We A )
7	2, 6	wb 184	1 wff ( Ord A <-> ( Tr A /\ _E We A ) )

This definition is referenced by:  ordeq  4872  ordwe  4878  ordtr  4879  trssord  4882  ordelord  4887  ord0  4917  ordon  6600  dford2  8037  smobeth  8961  gruina  9196  dford5reg  29186  dfon2  29196