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Definition df-tr 5262
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6103). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5263 (which is suggestive of the word "transitive"), dftr2c 5264, dftr3 5267, dftr4 5268, dftr5 5265, and (when 𝐴 is a set) unisuc 6435. 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 5261 . 2 wff Tr 𝐴
31cuni 4904 . . 3 class 𝐴
43, 1wss 3946 . 2 wff 𝐴𝐴
52, 4wb 205 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  5263  dftr4  5268  treq  5269  trv  5275  pwtr  5448  unisucg  6434  orduniss  6453  onuninsuci  7816  trcl  9710  tc2  9724  r1tr2  9759  tskuni  10765  untangtr  34614  hfuni  35087
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