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Definition df-tr 5260
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6130). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5261 (which is suggestive of the word "transitive"), dftr2c 5262, dftr3 5265, dftr4 5266, dftr5 5263, and (when 𝐴 is a set) unisuc 6463. 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 5259 . 2 wff Tr 𝐴
31cuni 4907 . . 3 class 𝐴
43, 1wss 3951 . 2 wff 𝐴𝐴
52, 4wb 206 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  5261  dftr4  5266  treq  5267  trv  5273  pwtr  5457  unisucg  6462  orduniss  6481  onuninsuci  7861  trcl  9768  tc2  9782  r1tr2  9817  tskuni  10823  untangtr  35714  hfuni  36185
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