Definition df-ord 5381

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 5377	. 2 wff Ord A
3	1	wtr 4454	. . 3 wff Tr A
4		cep 4698	. . . 4 class _E
5	1, 4	wwe 4747	. . 3 wff _E We A
6	3, 5	wa 370	. 2 wff ( Tr A /\ _E We A )
7	2, 6	wb 187	1 wff ( Ord A <-> ( Tr A /\ _E We A ) )

This definition is referenced by:  ordeq  5385  ordwe  5391  ordtr  5392  trssord  5395  ordelord  5400  ord0  5430  ordon  6560  dfrecs3  7039  dford2  8071  smobeth  8955  gruina  9187  dford5reg  30372  dfon2  30382