Definition df-trrels 39024

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 39032. Alternate definitions are dftrrels2 39026 and dftrrels3 39027.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38958) and symmetric (df-symrels 38990) 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 38564	. 2 class TrRels
2		ctrs 38563	. . 3 class Trs
3		crels 38552	. . 3 class Rels
4	2, 3	cin 3882	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1547	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  39026