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Definition df-tr 4947
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5718). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 4948 (which is suggestive of the word "transitive"), dftr3 4950, dftr4 4951, dftr5 4949, and (when 𝐴 is a set) unisuc 6013. 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 4946 . 2 wff Tr 𝐴
31cuni 4630 . . 3 class 𝐴
43, 1wss 3769 . 2 wff 𝐴𝐴
52, 4wb 197 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  4948  dftr4  4951  treq  4952  trv  4958  pwtr  5111  unisuc  6013  orduniss  6031  onuninsuci  7266  trcl  8847  tc2  8861  r1tr2  8883  tskuni  9886  untangtr  31908  hfuni  32607
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