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Definition df-tr 4897
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5658). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 4898 (which is suggestive of the word "transitive"), dftr3 4900, dftr4 4901, dftr5 4899, and (when 𝐴 is a set) unisuc 5954. 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 4896 . 2 wff Tr 𝐴
31cuni 4580 . . 3 class 𝐴
43, 1wss 3707 . 2 wff 𝐴𝐴
52, 4wb 196 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  4898  dftr4  4901  treq  4902  trv  4909  pwtr  5062  unisuc  5954  orduniss  5974  onuninsuci  7197  trcl  8769  tc2  8783  r1tr2  8805  tskuni  9789  untangtr  31890  hfuni  32589
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