Definition df-trrels 38555

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 38563. Alternate definitions are dftrrels2 38557 and dftrrels3 38558.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38493) and symmetric (df-symrels 38525) 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 38176	. 2 class TrRels
2		ctrs 38175	. . 3 class Trs
3		crels 38164	. . 3 class Rels
4	2, 3	cin 3962	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1537	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38557