Definition df-ord 2202

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 2198	. 2 wff Ord A
3	1	wtr 2041	. . 3 wff Tr A
4		cep 2056	. . . 4 class E
5	1, 4	wwe 2062	. . 3 wff E We A
6	3, 5	wa 196	. 2 wff (Tr A ∧ E We A)
7	2, 6	wb 127	1 wff (Ord A ↔ (Tr A ∧ E We A))

This definition is referenced by:  ordeq 2206  ordwe 2212  ordtr 2213  trssord 2216  ordelord 2221  ordon 2238  ord0 2276

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