Description: Equivalence relation implies that the domain and the range are equal. (Contributed by Peter Mazsa, 29-Dec-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | eqvrelim | |- ( EqvRel R -> dom R = ran R ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqvrelsymrel | |- ( EqvRel R -> SymRel R ) |
|
2 | symrelim | |- ( SymRel R -> dom R = ran R ) |
|
3 | 1 2 | syl | |- ( EqvRel R -> dom R = ran R ) |