Definition df-tr 5230

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6099). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5231 (which is suggestive of the word "transitive"), dftr2c 5232, dftr3 5235, dftr4 5236, dftr5 5233, and (when 𝐴 is a set) unisuc 6432. 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 5229	. 2 wff Tr 𝐴
3	1	cuni 4883	. . 3 class ∪ 𝐴
4	3, 1	wss 3926	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 206	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5231  dftr4  5236  treq  5237  trv  5243  pwtr  5427  unisucg  6431  orduniss  6450  onuninsuci  7833  trcl  9740  tc2  9754  r1tr2  9789  tskuni  10795  untangtr  35677  hfuni  36148