Description: Intersection of a closed subspace and its orthocomplement. Part of Proposition 1 of Kalmbach p. 65. (Contributed by NM, 11-Oct-1999) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | ch0le.1 | |- A e. CH |
|
| Assertion | chocini | |- ( A i^i ( _|_ ` A ) ) = 0H |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ch0le.1 | |- A e. CH |
|
| 2 | 1 | chshii | |- A e. SH |
| 3 | ocin | |- ( A e. SH -> ( A i^i ( _|_ ` A ) ) = 0H ) |
|
| 4 | 2 3 | ax-mp | |- ( A i^i ( _|_ ` A ) ) = 0H |