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| 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 38582.  Alternate definitions
     are dftrrels2 38576 and dftrrels3 38577. This definition is similar to the definitions of the classes of reflexive (df-refrels 38512) and symmetric (df-symrels 38544) relations. (Contributed by Peter Mazsa, 7-Jul-2019.) | 
| Ref | Expression | 
|---|---|
| df-trrels | ⊢ TrRels = ( Trs ∩ Rels ) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ctrrels 38196 | . 2 class TrRels | |
| 2 | ctrs 38195 | . . 3 class Trs | |
| 3 | crels 38184 | . . 3 class Rels | |
| 4 | 2, 3 | cin 3950 | . 2 class ( Trs ∩ Rels ) | 
| 5 | 1, 4 | wceq 1540 | 1 wff TrRels = ( Trs ∩ Rels ) | 
| Colors of variables: wff setvar class | 
| This definition is referenced by: dftrrels2 38576 | 
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