Definition df-ord 5449

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 5445	. 2 wff Ord A
3	1	wtr 4513	. . 3 wff Tr A
4		cep 4765	. . . 4 class _E
5	1, 4	wwe 4814	. . 3 wff _E We A
6	3, 5	wa 375	. 2 wff ( Tr A /\ _E We A )
7	2, 6	wb 189	1 wff ( Ord A <-> ( Tr A /\ _E We A ) )

This definition is referenced by:  ordeq  5453  ordwe  5459  ordtr  5460  trssord  5463  ordelord  5468  ord0  5498  ordon  6641  dfrecs3  7122  dford2  8156  smobeth  9042  gruina  9274  dford5reg  30478  dfon2  30488