Definition df-trrels 38571

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 38579. Alternate definitions are dftrrels2 38573 and dftrrels3 38574.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38509) and symmetric (df-symrels 38541) 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 38190	. 2 class TrRels
2		ctrs 38189	. . 3 class Trs
3		crels 38178	. . 3 class Rels
4	2, 3	cin 3916	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1540	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  38573