Definition df-tr 5204

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr 6067). Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 5205 (which is suggestive of the word "transitive"), dftr2c 5206, dftr3 5208, dftr4 5209, dftr5 5207, and (when 𝐴 is a set) unisuc 6396. 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 5203	. 2 wff Tr 𝐴
3	1	cuni 4861	. . 3 class ∪ 𝐴
4	3, 1	wss 3899	. 2 wff ∪ 𝐴 ⊆ 𝐴
5	2, 4	wb 206	1 wff (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)

This definition is referenced by:  dftr2  5205  dftr4  5209  treq  5210  trv  5216  pwtr  5398  unisucg  6395  orduniss  6414  onuninsuci  7780  trcl  9635  tc2  9647  r1tr2  9687  tskuni  10692  tz9.1regs  35239  untangtr  35857  hfuni  36327