Definition df-trrels 36614

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 36622. Alternate definitions are dftrrels2 36616 and dftrrels3 36617.

This definition is similar to the definitions of the classes of reflexive (df-refrels 36556) and symmetric (df-symrels 36584) 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 36274	. 2 class TrRels
2		ctrs 36273	. . 3 class Trs
3		crels 36262	. . 3 class Rels
4	2, 3	cin 3882	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1539	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  36616