Definition df-trrels 37529

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 37537. Alternate definitions are dftrrels2 37531 and dftrrels3 37532.

This definition is similar to the definitions of the classes of reflexive (df-refrels 37467) and symmetric (df-symrels 37499) 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 37143	. 2 class TrRels
2		ctrs 37142	. . 3 class Trs
3		crels 37131	. . 3 class Rels
4	2, 3	cin 3947	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1541	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  37531