Definition df-trrels 38830

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 38838. Alternate definitions are dftrrels2 38832 and dftrrels3 38833.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38764) and symmetric (df-symrels 38796) 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 38397	. 2 class TrRels
2		ctrs 38396	. . 3 class Trs
3		crels 38385	. . 3 class Rels
4	2, 3	cin 3900	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1541	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38832