Description: Define the class of all complex Hilbert spaces. A Hilbert space is a Banach space which is also an inner product space. (Contributed by Steve Rodriguez, 28-Apr-2007) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | df-hlo | |- CHilOLD = ( CBan i^i CPreHilOLD ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | chlo | |- CHilOLD |
|
1 | ccbn | |- CBan |
|
2 | ccphlo | |- CPreHilOLD |
|
3 | 1 2 | cin | |- ( CBan i^i CPreHilOLD ) |
4 | 0 3 | wceq | |- CHilOLD = ( CBan i^i CPreHilOLD ) |