Definition df-trrels

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 . Alternate definitions are dftrrels2 and dftrrels3 .

This definition is similar to the definitions of the classes of reflexive ( df-refrels ) and symmetric ( df-symrels ) relations. (Contributed by Peter Mazsa, 7-Jul-2019)

	Ref	Expression
Assertion	df-trrels	$$⊢\mathrm{TrRels}=\mathrm{Trs}\cap \mathrm{Rels}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		ctrrels	$$class\mathrm{TrRels}$$
1		ctrs	$$class\mathrm{Trs}$$
2		crels	$$class\mathrm{Rels}$$
3	1 2	cin	$$class\left(\mathrm{Trs}\cap \mathrm{Rels}\right)$$
4	0 3	wceq	$$wff\mathrm{TrRels}=\mathrm{Trs}\cap \mathrm{Rels}$$