Definition df-trrels 39334

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 39342. Alternate definitions are dftrrels2 39336 and dftrrels3 39337.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39268) and symmetric (df-symrels 39300) 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 38874	. 2 class TrRels
2		ctrs 38873	. . 3 class Trs
3		crels 38862	. . 3 class Rels
4	2, 3	cin 3904	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1570	1 wff TrRels = ( Trs ∩ Rels )

This definition is used by:  dftrrels2  39336