Definition df-trrels 38271

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 38279. Alternate definitions are dftrrels2 38273 and dftrrels3 38274.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38209) and symmetric (df-symrels 38241) 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 37890	. 2 class TrRels
2		ctrs 37889	. . 3 class Trs
3		crels 37878	. . 3 class Rels
4	2, 3	cin 3946	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1534	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38273