Definition df-trrels 39405

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 39413. Alternate definitions are dftrrels2 39407 and dftrrels3 39408.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39339) and symmetric (df-symrels 39371) 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 38945	. 2 class TrRels
2		ctrs 38944	. . 3 class Trs
3		crels 38933	. . 3 class Rels
4	2, 3	cin 3898	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1570	1 wff TrRels = ( Trs ∩ Rels )

This definition is used by:  dftrrels2  39407