Definition df-trrels 38574

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 38582. Alternate definitions are dftrrels2 38576 and dftrrels3 38577.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38512) and symmetric (df-symrels 38544) 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 38196	. 2 class TrRels
2		ctrs 38195	. . 3 class Trs
3		crels 38184	. . 3 class Rels
4	2, 3	cin 3950	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1540	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38576