Description: No Hilbert closed subspace is smaller than zero. (Contributed by NM, 7-Apr-2001) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ch0le.1 | |- A e. CH |
|
Assertion | chle0i | |- ( A C_ 0H <-> A = 0H ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ch0le.1 | |- A e. CH |
|
2 | chle0 | |- ( A e. CH -> ( A C_ 0H <-> A = 0H ) ) |
|
3 | 1 2 | ax-mp | |- ( A C_ 0H <-> A = 0H ) |