Definition df-tr 5200

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6061). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5201 (which is suggestive of the word "transitive"), dftr2c 5202, dftr3 5204, dftr4 5205, dftr5 5203, and (when 𝐴 is a set) unisuc 6388. 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 5199	. 2 wff Tr 𝐴
3	1	cuni 4858	. . 3 class ∪ 𝐴
4	3, 1	wss 3903	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 206	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5201  dftr4  5205  treq  5206  trv  5212  pwtr  5395  unisucg  6387  orduniss  6406  onuninsuci  7773  trcl  9624  tc2  9638  r1tr2  9673  tskuni  10677  tz9.1regs  35073  untangtr  35697  hfuni  36168