Definition df-ord 4870

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 4866	. 2 wff Ord A
3	1	wtr 4532	. . 3 wff Tr A
4		cep 4778	. . . 4 class _E
5	1, 4	wwe 4826	. . 3 wff _E We A
6	3, 5	wa 367	. 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  4874  ordwe  4880  ordtr  4881  trssord  4884  ordelord  4889  ord0  4919  ordon  6591  dford2  8028  smobeth  8952  gruina  9185  dford5reg  29454  dfon2  29464