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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 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.) |
Ref | Expression |
---|---|
df-trrels | ⊢ TrRels = ( Trs ∩ Rels ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ctrrels 36677 | . 2 class TrRels | |
2 | ctrs 36676 | . . 3 class Trs | |
3 | crels 36665 | . . 3 class Rels | |
4 | 2, 3 | cin 3914 | . 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 37066 |
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