Definition df-tr 5262

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6103). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5263 (which is suggestive of the word "transitive"), dftr2c 5264, dftr3 5267, dftr4 5268, dftr5 5265, and (when 𝐴 is a set) unisuc 6435. 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 5261	. 2 wff Tr 𝐴
3	1	cuni 4904	. . 3 class ∪ 𝐴
4	3, 1	wss 3946	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 205	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5263  dftr4  5268  treq  5269  trv  5275  pwtr  5448  unisucg  6434  orduniss  6453  onuninsuci  7816  trcl  9710  tc2  9724  r1tr2  9759  tskuni  10765  untangtr  34614  hfuni  35087