Definition df-trrels 38905

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 38913. Alternate definitions are dftrrels2 38907 and dftrrels3 38908.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38839) and symmetric (df-symrels 38871) 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 38445	. 2 class TrRels
2		ctrs 38444	. . 3 class Trs
3		crels 38433	. . 3 class Rels
4	2, 3	cin 3902	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1542	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38907