Definition df-trrels 36687

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 36695. Alternate definitions are dftrrels2 36689 and dftrrels3 36690.

This definition is similar to the definitions of the classes of reflexive (df-refrels 36629) and symmetric (df-symrels 36657) 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 36347	. 2 class TrRels
2		ctrs 36346	. . 3 class Trs
3		crels 36335	. . 3 class Rels
4	2, 3	cin 3886	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1539	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  36689