Definition df-tr 5215

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6083). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5216 (which is suggestive of the word "transitive"), dftr2c 5217, dftr3 5220, dftr4 5221, dftr5 5218, and (when 𝐴 is a set) unisuc 6413. 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 5214	. 2 wff Tr 𝐴
3	1	cuni 4871	. . 3 class ∪ 𝐴
4	3, 1	wss 3914	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 206	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5216  dftr4  5221  treq  5222  trv  5228  pwtr  5412  unisucg  6412  orduniss  6431  onuninsuci  7816  trcl  9681  tc2  9695  r1tr2  9730  tskuni  10736  untangtr  35701  hfuni  36172