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Definition df-trrels 37064
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 37072. Alternate definitions are dftrrels2 37066 and dftrrels3 37067.

This definition is similar to the definitions of the classes of reflexive (df-refrels 37002) and symmetric (df-symrels 37034) 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 36677 . 2 class TrRels
2 ctrs 36676 . . 3 class Trs
3 crels 36665 . . 3 class Rels
42, 3cin 3914 . 2 class ( Trs ∩ Rels )
51, 4wceq 1542 1 wff TrRels = ( Trs ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dftrrels2  37066
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