Definition df-trrels 39117

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 39125. Alternate definitions are dftrrels2 39119 and dftrrels3 39120.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39051) and symmetric (df-symrels 39083) 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 38657	. 2 class TrRels
2		ctrs 38656	. . 3 class Trs
3		crels 38645	. . 3 class Rels
4	2, 3	cin 3901	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1559	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  39119