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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-trrels | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
df-trrels | ⊢ TrRels = ( Trs ∩ Rels ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ctrrels 36580 | . 2 class TrRels | |
2 | ctrs 36579 | . . 3 class Trs | |
3 | crels 36568 | . . 3 class Rels | |
4 | 2, 3 | cin 3908 | . 2 class ( Trs ∩ Rels ) |
5 | 1, 4 | wceq 1542 | 1 wff TrRels = ( Trs ∩ Rels ) |
Colors of variables: wff setvar class |
This definition is referenced by: dftrrels2 36969 |
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