Definition df-tr 5208

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6079). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5209 (which is suggestive of the word "transitive"), dftr2c 5210, dftr3 5212, dftr4 5213, dftr5 5211, and (when 𝐴 is a set) unisuc 6408. 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 5207	. 2 wff Tr 𝐴
3	1	cuni 4865	. . 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  5209  dftr4  5213  treq  5214  trv  5220  pwtr  5409  unisucg  6407  orduniss  6426  onuninsuci  7794  trcl  9651  tc2  9663  r1tr2  9703  tskuni  10708  tz9.1regs  35318  untangtr  35936  hfuni  36406