Definition df-tr 4897

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5658). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 4898 (which is suggestive of the word "transitive"), dftr3 4900, dftr4 4901, dftr5 4899, and (when 𝐴 is a set) unisuc 5954. 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 4896	. 2 wff Tr 𝐴
3	1	cuni 4580	. . 3 class ∪ 𝐴
4	3, 1	wss 3707	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 196	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  4898  dftr4  4901  treq  4902  trv  4909  pwtr  5062  unisuc  5954  orduniss  5974  onuninsuci  7197  trcl  8769  tc2  8783  r1tr2  8805  tskuni  9789  untangtr  31890  hfuni  32589