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Definition df-iord 4048
Description: Define the ordinal predicate, which is true for a class that is transitive and whose elements are transitive. Definition of ordinal in [Crosilla], p. "Set-theoretic principles incompatible with intuitionistic logic". (Contributed by Jim Kingdon, 10-Oct-2018.) Use its alias dford3 4049 instead for naming consistency with set.mm. (New usage is discouraged.)
Assertion
Ref Expression
df-iord (Ord A ↔ (Tr A x A Tr x))
Distinct variable group:   x,A

Detailed syntax breakdown of Definition df-iord
StepHypRef Expression
1 cA . . 3 class A
21word 4044 . 2 wff Ord A
31wtr 3824 . . 3 wff Tr A
4 vx . . . . . 6 setvar x
54cv 1225 . . . . 5 class x
65wtr 3824 . . . 4 wff Tr x
76, 4, 1wral 2280 . . 3 wff x A Tr x
83, 7wa 97 . 2 wff (Tr A x A Tr x)
92, 8wb 98 1 wff (Ord A ↔ (Tr A x A Tr x))
Colors of variables: wff set class
This definition is referenced by:  dford3  4049
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