Definition df-trrels 39569

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 39577. Alternate definitions are dftrrels2 39571 and dftrrels3 39572.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39503) and symmetric (df-symrels 39535) 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 39109	. 2 class TrRels
2		ctrs 39108	. . 3 class Trs
3		crels 39097	. . 3 class Rels
4	2, 3	cin 3898	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1570	1 wff TrRels = ( Trs ∩ Rels )

This definition is used by:  dftrrels2  39571