Definition df-trrels 38992

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 39000. Alternate definitions are dftrrels2 38994 and dftrrels3 38995.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38926) and symmetric (df-symrels 38958) 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 38532	. 2 class TrRels
2		ctrs 38531	. . 3 class Trs
3		crels 38520	. . 3 class Rels
4	2, 3	cin 3889	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1542	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38994