Definition df-trrels 39855

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 39863. Alternate definitions are dftrrels2 39857 and dftrrels3 39858.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39789) and symmetric (df-symrels 39821) 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 39395	. 2 class TrRels
2		ctrs 39394	. . 3 class Trs
3		crels 39383	. . 3 class Rels
4	2, 3	cin 4092	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1570	1 wff TrRels = ( Trs ∩ Rels )

This definition is used by:  dftrrels2  39857