Definition df-tr 4102

Description: Define the transitive class predicate. Definition of [Enderton] p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 4103 (which is suggestive of the word "transitive"), dftr3 4105, dftr4 4106, and dftr5 4104. 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 <-> U. A C_ A )

Detailed syntax breakdown of Definition df-tr

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	wtr 4101	. 2 wff Tr A
3	1	cuni 3809	. . 3 class U. A
4	3, 1	wss 3129	. 2 wff U. A C_ A
5	2, 4	wb 105	1 wff ( Tr A <-> U. A C_ A )

This definition is referenced by:  dftr2  4103  dftr4  4106  treq  4107  trv  4113  pwtr  4219  unisuc  4413  unisucg  4414  orduniss  4425