Definition df-tr 5284

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6142). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5285 (which is suggestive of the word "transitive"), dftr2c 5286, dftr3 5289, dftr4 5290, dftr5 5287, and (when 𝐴 is a set) unisuc 6474. 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 5283	. 2 wff Tr 𝐴
3	1	cuni 4931	. . 3 class ∪ 𝐴
4	3, 1	wss 3976	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 206	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5285  dftr4  5290  treq  5291  trv  5297  pwtr  5472  unisucg  6473  orduniss  6492  onuninsuci  7877  trcl  9797  tc2  9811  r1tr2  9846  tskuni  10852  untangtr  35676  hfuni  36148