Definition df-ord 3660

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.

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 3656	. 2 wff Ord A
3	1	wtr 3411	. . 3 wff Tr A
4		cep 3581	. . . 4 class _E
5	1, 4	wwe 3624	. . 3 wff _E We A
6	3, 5	wa 240	. 2 wff (Tr A /\ _E We A)
7	2, 6	wb 163	1 wff (Ord A <-> (Tr A /\ _E We A))

This definition is referenced by:  ordeq 3664  ordwe 3671  ordtr 3672  trssord 3675  ordelord 3680  ord0 3715  ordon 3863  dford2 5711  dford3 13848  dfon2 13858  tfrALTlem 13976  tartord 15240

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