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Definition df-tr 4723
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5477). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 4724 (which is suggestive of the word "transitive"), dftr3 4726, dftr4 4727, dftr5 4725, and (when 𝐴 is a set) unisuc 5770. 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 4722 . 2 wff Tr 𝐴
31cuni 4409 . . 3 class 𝐴
43, 1wss 3560 . 2 wff 𝐴𝐴
52, 4wb 196 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  4724  dftr4  4727  treq  4728  trv  4735  pwtr  4892  unisuc  5770  orduniss  5790  onuninsuci  7002  trcl  8564  tc2  8578  r1tr2  8600  tskuni  9565  untangtr  31352  hfuni  31986
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