Definition df-trrels 39306

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 39314. Alternate definitions are dftrrels2 39308 and dftrrels3 39309.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39240) and symmetric (df-symrels 39272) 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 38846	. 2 class TrRels
2		ctrs 38845	. . 3 class Trs
3		crels 38834	. . 3 class Rels
4	2, 3	cin 3904	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1570	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  39308