Definition df-ord 2946

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 2942	. 2 wff Ord A
3	1	wtr 2675	. . 3 wff Tr A
4		cep 2825	. . . 4 class E
5	1, 4	wwe 2911	. . 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 2950  ordwe 2956  ordtr 2957  trssord 2960  ordelord 2965  ordon 2982  ord0 3016

Copyright terms: Public domain