Definition df-trrels 35824

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 35832. Alternate definitions are dftrrels2 35826 and dftrrels3 35827.

This definition is similar to the definitions of the classes of reflexive (df-refrels 35766) and symmetric (df-symrels 35794) 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 35482	. 2 class TrRels
2		ctrs 35481	. . 3 class Trs
3		crels 35470	. . 3 class Rels
4	2, 3	cin 3935	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1537	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  35826