Definition df-tr 3846

Description: Define the transitive class predicate. Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 3847 (which is suggestive of the word "transitive"), dftr3 3849, dftr4 3850, and dftr5 3848. 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 3845	. 2 wff Tr A
3	1	cuni 3571	. . 3 class ∪ A
4	3, 1	wss 2911	. 2 wff ∪ A ⊆ A
5	2, 4	wb 98	1 wff (Tr A ↔ ∪ A ⊆ A)

This definition is referenced by:  dftr2  3847  dftr4  3850  treq  3851  trv  3857  pwtr  3946  unisuc  4116  unisucg  4117  orduniss  4128