Definition df-trrels 39191

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 39199. Alternate definitions are dftrrels2 39193 and dftrrels3 39194.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39125) and symmetric (df-symrels 39157) 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 38731	. 2 class TrRels
2		ctrs 38730	. . 3 class Trs
3		crels 38719	. . 3 class Rels
4	2, 3	cin 3912	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1567	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  39193