Definition df-trrels 38552

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 38560. Alternate definitions are dftrrels2 38554 and dftrrels3 38555.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38490) and symmetric (df-symrels 38522) 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 38171	. 2 class TrRels
2		ctrs 38170	. . 3 class Trs
3		crels 38159	. . 3 class Rels
4	2, 3	cin 3904	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1540	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38554