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Definition df-tr 5160
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5961). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5161 (which is suggestive of the word "transitive"), dftr3 5163, dftr4 5164, dftr5 5162, and (when 𝐴 is a set) unisuc 6256. 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 5159 . 2 wff Tr 𝐴
31cuni 4824 . . 3 class 𝐴
43, 1wss 3919 . 2 wff 𝐴𝐴
52, 4wb 209 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  5161  dftr4  5164  treq  5165  trv  5171  pwtr  5333  unisuc  6256  orduniss  6274  onuninsuci  7551  trcl  9169  tc2  9183  r1tr2  9205  tskuni  10205  untangtr  33025  hfuni  33730
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