Definition df-ord 2941

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 2937	. 2 wff Ord A
3	1	wtr 2670	. . 3 wff Tr A
4		cep 2819	. . . 4 class E
5	1, 4	wwe 2906	. . 3 wff E We A
6	3, 5	wa 223	. 2 wff (Tr A /\ E We A)
7	2, 6	wb 146	1 wff (Ord A <-> (Tr A /\ E We A))

This definition is referenced by:  ordeq 2945  ordwe 2951  ordtr 2952  trssord 2955  ordelord 2960  ordon 2977  ord0 3011

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