Definition df-trrels 39339

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 39347. Alternate definitions are dftrrels2 39341 and dftrrels3 39342.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39273) and symmetric (df-symrels 39305) 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 38879	. 2 class TrRels
2		ctrs 38878	. . 3 class Trs
3		crels 38867	. . 3 class Rels
4	2, 3	cin 3905	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1570	1 wff TrRels = ( Trs ∩ Rels )

This definition is used by:  dftrrels2  39341