Definition df-ord 5436

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 5432	. 2 wff Ord A
3	1	wtr 4511	. . 3 wff Tr A
4		cep 4754	. . . 4 class _E
5	1, 4	wwe 4803	. . 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  5440  ordwe  5446  ordtr  5447  trssord  5450  ordelord  5455  ord0  5485  ordon  6614  dfrecs3  7090  dford2  8116  smobeth  9000  gruina  9232  dford5reg  30212  dfon2  30222