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Definition df-trrels 36967
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 36975. Alternate definitions are dftrrels2 36969 and dftrrels3 36970.

This definition is similar to the definitions of the classes of reflexive (df-refrels 36905) and symmetric (df-symrels 36937) relations. (Contributed by Peter Mazsa, 7-Jul-2019.)

Assertion
Ref Expression
df-trrels TrRels = ( Trs ∩ Rels )

Detailed syntax breakdown of Definition df-trrels
StepHypRef Expression
1 ctrrels 36580 . 2 class TrRels
2 ctrs 36579 . . 3 class Trs
3 crels 36568 . . 3 class Rels
42, 3cin 3908 . 2 class ( Trs ∩ Rels )
51, 4wceq 1542 1 wff TrRels = ( Trs ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dftrrels2  36969
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