Definition df-tr 5173

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5972). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5174 (which is suggestive of the word "transitive"), dftr3 5176, dftr4 5177, dftr5 5175, and (when 𝐴 is a set) unisuc 6267. 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 5172	. 2 wff Tr 𝐴
3	1	cuni 4838	. . 3 class ∪ 𝐴
4	3, 1	wss 3936	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 208	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5174  dftr4  5177  treq  5178  trv  5184  pwtr  5345  unisuc  6267  orduniss  6285  onuninsuci  7555  trcl  9170  tc2  9184  r1tr2  9206  tskuni  10205  untangtr  32940  hfuni  33645