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Definition df-tr 4681
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5427). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 4682 (which is suggestive of the word "transitive"), dftr3 4684, dftr4 4685, dftr5 4683, and (when 𝐴 is a set) unisuc 5718. 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 4680 . 2 wff Tr 𝐴
31cuni 4372 . . 3 class 𝐴
43, 1wss 3540 . 2 wff 𝐴𝐴
52, 4wb 195 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  4682  dftr4  4685  treq  4686  trv  4693  pwtr  4848  unisuc  5718  orduniss  5738  onuninsuci  6932  trcl  8487  tc2  8501  r1tr2  8523  tskuni  9484  untangtr  30845  hfuni  31461
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