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 . Alternate definitions are dftrrels2 and dftrrels3 .
This definition is similar to the definitions of the classes of reflexive ( df-refrels ) and symmetric ( df-symrels ) relations. (Contributed by Peter Mazsa, 7-Jul-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | df-trrels |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | ctrrels | ||
1 | ctrs | ||
2 | crels | ||
3 | 1 2 | cin | |
4 | 0 3 | wceq |