Definition df-trrels 39696

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 39704. Alternate definitions are dftrrels2 39698 and dftrrels3 39699.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39630) and symmetric (df-symrels 39662) 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 39236	. 2 class TrRels
2		ctrs 39235	. . 3 class Trs
3		crels 39224	. . 3 class Rels
4	2, 3	cin 4088	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1569	1 wff TrRels = ( Trs ∩ Rels )

This definition is used by:  dftrrels2  39698