Definition df-trrels 38529

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 38537. Alternate definitions are dftrrels2 38531 and dftrrels3 38532.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38467) and symmetric (df-symrels 38499) 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 38149	. 2 class TrRels
2		ctrs 38148	. . 3 class Trs
3		crels 38137	. . 3 class Rels
4	2, 3	cin 3975	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1537	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38531