Definition df-trrels 37747

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 37755. Alternate definitions are dftrrels2 37749 and dftrrels3 37750.

This definition is similar to the definitions of the classes of reflexive (df-refrels 37685) and symmetric (df-symrels 37717) 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 37361	. 2 class TrRels
2		ctrs 37360	. . 3 class Trs
3		crels 37349	. . 3 class Rels
4	2, 3	cin 3948	. 2 class ( Trs ∩ Rels )
5	1, 4	wceq 1540	1 wff TrRels = ( Trs ∩ Rels )

This definition is referenced by:  dftrrels2  37749