Description: Alternate definition of the class of symmetric relations. (Contributed by Peter Mazsa, 22-Jul-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | dfsymrels5 | |- SymRels = { r e. Rels | A. x A. y ( x r y <-> y r x ) } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsymrels4 | |- SymRels = { r e. Rels | `' r = r } |
|
2 | elrelscnveq2 | |- ( r e. Rels -> ( `' r = r <-> A. x A. y ( x r y <-> y r x ) ) ) |
|
3 | 1 2 | rabimbieq | |- SymRels = { r e. Rels | A. x A. y ( x r y <-> y r x ) } |