Definition df-ord 4544

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 4540	. 2 wff Ord A
3	1	wtr 4262	. . 3 wff Tr A
4		cep 4452	. . . 4 class _E
5	1, 4	wwe 4500	. . 3 wff _E We A
6	3, 5	wa 359	. 2 wff ( Tr A /\ _E We A )
7	2, 6	wb 177	1 wff ( Ord A <-> ( Tr A /\ _E We A ) )

This definition is referenced by:  ordeq  4548  ordwe  4554  ordtr  4555  trssord  4558  ordelord  4563  ord0  4593  ordon  4722  dford2  7531  smobeth  8417  gruina  8649  dford5reg  25352  dfon2  25362  tfrALTlem  25490