Definition df-trrels 37108

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 37116. Alternate definitions are dftrrels2 37110 and dftrrels3 37111.

This definition is similar to the definitions of the classes of reflexive (df-refrels 37046) and symmetric (df-symrels 37078) 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 36721	. 2 class TrRels
2		ctrs 36720	. . 3 class Trs
3		crels 36709	. . 3 class Rels
4	2, 3	cin 3912	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1541	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  37110