Definition df-tr 3818

Description: Define the transitive class predicate. Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 3819 (which is suggestive of the word "transitive"), dftr3 3821, dftr4 3822, and dftr5 3820. 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 3817	. 2 wff Tr A
3	1	cuni 3543	. . 3 class ∪ A
4	3, 1	wss 2885	. 2 wff ∪ A ⊆ A
5	2, 4	wb 98	1 wff (Tr A ↔ ∪ A ⊆ A)

This definition is referenced by:  dftr2  3819  dftr4  3822  treq  3823  trv  3829  pwtr  3918  unisuc  4088  unisucg  4089  orduniss  4100