Definition df-tr 5207

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6070). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5208 (which is suggestive of the word "transitive"), dftr2c 5209, dftr3 5211, dftr4 5212, dftr5 5210, and (when 𝐴 is a set) unisuc 6399. 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 5206	. 2 wff Tr 𝐴
3	1	cuni 4864	. . 3 class ∪ 𝐴
4	3, 1	wss 3902	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 206	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5208  dftr4  5212  treq  5213  trv  5219  pwtr  5401  unisucg  6398  orduniss  6417  onuninsuci  7784  trcl  9641  tc2  9653  r1tr2  9693  tskuni  10698  tz9.1regs  35292  untangtr  35910  hfuni  36380