Description: Define the class of symmetric relations. For sets, being an element of the class of symmetric relations is equivalent to satisfying the symmetric relation predicate, see elsymrelsrel . Alternate definitions are dfsymrels2 , dfsymrels3 , dfsymrels4 and dfsymrels5 .
This definition is similar to the definitions of the classes of reflexive ( df-refrels ) and transitive ( df-trrels ) relations. (Contributed by Peter Mazsa, 7-Jul-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | df-symrels | |- SymRels = ( Syms i^i Rels ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | csymrels | |- SymRels |
|
1 | csyms | |- Syms |
|
2 | crels | |- Rels |
|
3 | 1 2 | cin | |- ( Syms i^i Rels ) |
4 | 0 3 | wceq | |- SymRels = ( Syms i^i Rels ) |