Definition df-trrels 38616

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 38624. Alternate definitions are dftrrels2 38618 and dftrrels3 38619.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38554) and symmetric (df-symrels 38586) 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 38235	. 2 class TrRels
2		ctrs 38234	. . 3 class Trs
3		crels 38223	. . 3 class Rels
4	2, 3	cin 3901	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1541	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38618