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Definition df-tr 4786
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5543). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 4787 (which is suggestive of the word "transitive"), dftr3 4789, dftr4 4790, dftr5 4788, and (when 𝐴 is a set) unisuc 5839. 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 4785 . 2 wff Tr 𝐴
31cuni 4468 . . 3 class 𝐴
43, 1wss 3607 . 2 wff 𝐴𝐴
52, 4wb 196 1 wff (Tr 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dftr2  4787  dftr4  4790  treq  4791  trv  4798  pwtr  4951  unisuc  5839  orduniss  5859  onuninsuci  7082  trcl  8642  tc2  8656  r1tr2  8678  tskuni  9643  untangtr  31717  hfuni  32416
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