Definition df-tr 5267

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6112). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5268 (which is suggestive of the word "transitive"), dftr2c 5269, dftr3 5272, dftr4 5273, dftr5 5270, and (when 𝐴 is a set) unisuc 6444. 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 5266	. 2 wff Tr 𝐴
3	1	cuni 4909	. . 3 class ∪ 𝐴
4	3, 1	wss 3949	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 205	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5268  dftr4  5273  treq  5274  trv  5280  pwtr  5453  unisucg  6443  orduniss  6462  onuninsuci  7829  trcl  9723  tc2  9737  r1tr2  9772  tskuni  10778  untangtr  34683  hfuni  35156