Description: A binary relation does not contain the empty set. (Contributed by AV, 15-Nov-2021) (Revised by BJ, 14-Jul-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | 0nelrel0 | |- ( Rel R -> -. (/) e. R ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rel | |- ( Rel R <-> R C_ ( _V X. _V ) ) |
|
2 | 1 | biimpi | |- ( Rel R -> R C_ ( _V X. _V ) ) |
3 | 0nelxp | |- -. (/) e. ( _V X. _V ) |
|
4 | 3 | a1i | |- ( Rel R -> -. (/) e. ( _V X. _V ) ) |
5 | 2 4 | ssneldd | |- ( Rel R -> -. (/) e. R ) |