Definition df-trrels 38591

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 38599. Alternate definitions are dftrrels2 38593 and dftrrels3 38594.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38529) and symmetric (df-symrels 38561) 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 38213	. 2 class TrRels
2		ctrs 38212	. . 3 class Trs
3		crels 38201	. . 3 class Rels
4	2, 3	cin 3925	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1540	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38593