Definition df-trrels 38564

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 38572. Alternate definitions are dftrrels2 38566 and dftrrels3 38567.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38502) and symmetric (df-symrels 38534) 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 38183	. 2 class TrRels
2		ctrs 38182	. . 3 class Trs
3		crels 38171	. . 3 class Rels
4	2, 3	cin 3913	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1540	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38566