Definition df-tr 5031

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 5812). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5032 (which is suggestive of the word "transitive"), dftr3 5034, dftr4 5035, dftr5 5033, and (when 𝐴 is a set) unisuc 6105. 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 5030	. 2 wff Tr 𝐴
3	1	cuni 4712	. . 3 class ∪ 𝐴
4	3, 1	wss 3829	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 198	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5032  dftr4  5035  treq  5036  trv  5042  pwtr  5202  unisuc  6105  orduniss  6123  onuninsuci  7371  trcl  8964  tc2  8978  r1tr2  9000  tskuni  10003  untangtr  32466  hfuni  33172