Definition df-trrels 38692

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 38700. Alternate definitions are dftrrels2 38694 and dftrrels3 38695.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38626) and symmetric (df-symrels 38658) 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 38259	. 2 class TrRels
2		ctrs 38258	. . 3 class Trs
3		crels 38247	. . 3 class Rels
4	2, 3	cin 3897	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1541	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38694