Definition df-tr 3825

Description: Define the transitive class predicate. Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 3826 (which is suggestive of the word "transitive"), dftr3 3828, dftr4 3829, and dftr5 3827. 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 3824	. 2 wff Tr A
3	1	cuni 3550	. . 3 class ∪ A
4	3, 1	wss 2890	. 2 wff ∪ A ⊆ A
5	2, 4	wb 98	1 wff (Tr A ↔ ∪ A ⊆ A)

This definition is referenced by:  dftr2  3826  dftr4  3829  treq  3830  trv  3836  pwtr  3925  unisuc  4095  unisucg  4096  orduniss  4108