Definition df-tr 5186

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6005). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5187 (which is suggestive of the word "transitive"), dftr3 5189, dftr4 5190, dftr5 5188, and (when 𝐴 is a set) unisuc 6324. 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 ↔ ∪ 𝐴 ⊆ 𝐴)

Detailed syntax breakdown of Definition df-tr

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2	1	wtr 5185	. 2 wff Tr 𝐴
3	1	cuni 4836	. . 3 class ∪ 𝐴
4	3, 1	wss 3884	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 209	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5187  dftr4  5190  treq  5191  trv  5197  pwtr  5361  unisuc  6324  orduniss  6342  onuninsuci  7659  trcl  9392  tc2  9406  r1tr2  9441  tskuni  10445  untangtr  33530  hfuni  34388