Definition df-trrels 36249

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 36257. Alternate definitions are dftrrels2 36251 and dftrrels3 36252.

This definition is similar to the definitions of the classes of reflexive (df-refrels 36191) and symmetric (df-symrels 36219) 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 35907	. 2 class TrRels
2		ctrs 35906	. . 3 class Trs
3		crels 35895	. . 3 class Rels
4	2, 3	cin 3857	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1538	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  36251