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Definition df-tr 5165
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5966). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5166 (which is suggestive of the word "transitive"), dftr3 5168, dftr4 5169, dftr5 5167, and (when 𝐴 is a set) unisuc 6261. The term "complete" is used instead of "transitive" in Definition 3 of [Suppes] p. 130. (Contributed by NM, 29-Aug-1993.)
Assertion
Ref Expression
df-tr (Tr 𝐴 𝐴𝐴)

Detailed syntax breakdown of Definition df-tr
StepHypRef Expression
1 cA . . 3 class 𝐴
21wtr 5164 . 2 wff Tr 𝐴
31cuni 4832 . . 3 class 𝐴
43, 1wss 3935 . 2 wff 𝐴𝐴
52, 4wb 207 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  5166  dftr4  5169  treq  5170  trv  5176  pwtr  5337  unisuc  6261  orduniss  6279  onuninsuci  7543  trcl  9159  tc2  9173  r1tr2  9195  tskuni  10194  untangtr  32838  hfuni  33543
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