Definition df-trrels 38589

Description: Define the class of transitive relations. For sets, being an element of the class of transitive relations is equivalent to satisfying the transitive relation predicate, see eltrrelsrel 38597. Alternate definitions are dftrrels2 38591 and dftrrels3 38592.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38527) and symmetric (df-symrels 38559) relations. (Contributed by Peter Mazsa, 7-Jul-2019.)

Assertion

Ref	Expression
df-trrels	⊢ TrRels = ( Trs ∩ Rels )

Detailed syntax breakdown of Definition df-trrels

Step	Hyp	Ref	Expression
1		ctrrels 38208	. 2 class TrRels
2		ctrs 38207	. . 3 class Trs
3		crels 38196	. . 3 class Rels
4	2, 3	cin 3899	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1541	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38591