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Definition df-tr 4263
Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5205). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 4264 (which is suggestive of the word "transitive"), dftr3 4266, dftr4 4267, dftr5 4265, and (when  A is a set) unisuc 4617. 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  <->  U. A  C_  A
)

Detailed syntax breakdown of Definition df-tr
StepHypRef Expression
1 cA . . 3  class  A
21wtr 4262 . 2  wff  Tr  A
31cuni 3975 . . 3  class  U. A
43, 1wss 3280 . 2  wff  U. A  C_  A
52, 4wb 177 1  wff  ( Tr  A  <->  U. A  C_  A
)
Colors of variables: wff set class
This definition is referenced by:  dftr2  4264  dftr4  4267  treq  4268  trv  4274  pwtr  4376  unisuc  4617  orduniss  4635  onuninsuci  4779  trcl  7620  tc2  7637  r1tr2  7659  tskuni  8614  untangtr  25116  hfuni  26029
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