Definition df-tr 5260

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6130). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5261 (which is suggestive of the word "transitive"), dftr2c 5262, dftr3 5265, dftr4 5266, dftr5 5263, and (when 𝐴 is a set) unisuc 6463. 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 5259	. 2 wff Tr 𝐴
3	1	cuni 4907	. . 3 class ∪ 𝐴
4	3, 1	wss 3951	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 206	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5261  dftr4  5266  treq  5267  trv  5273  pwtr  5457  unisucg  6462  orduniss  6481  onuninsuci  7861  trcl  9768  tc2  9782  r1tr2  9817  tskuni  10823  untangtr  35714  hfuni  36185