Definition df-tr 5210

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6071). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5211 (which is suggestive of the word "transitive"), dftr2c 5212, dftr3 5215, dftr4 5216, dftr5 5213, and (when 𝐴 is a set) unisuc 6401. 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 5209	. 2 wff Tr 𝐴
3	1	cuni 4867	. . 3 class ∪ 𝐴
4	3, 1	wss 3911	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 206	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5211  dftr4  5216  treq  5217  trv  5223  pwtr  5407  unisucg  6400  orduniss  6419  onuninsuci  7796  trcl  9657  tc2  9671  r1tr2  9706  tskuni  10712  untangtr  35694  hfuni  36165