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Mirrors > Home > MPE Home > Th. List > df-hl | Structured version Visualization version GIF version |
Description: Define the class of all complex Hilbert spaces. A complex Hilbert space is a Banach space which is also an inner product space over the complex numbers. (Contributed by Steve Rodriguez, 28-Apr-2007.) |
Ref | Expression |
---|---|
df-hl | ⊢ ℂHil = (Ban ∩ ℂPreHil) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chl 22939 | . 2 class ℂHil | |
2 | cbn 22938 | . . 3 class Ban | |
3 | ccph 22774 | . . 3 class ℂPreHil | |
4 | 2, 3 | cin 3539 | . 2 class (Ban ∩ ℂPreHil) |
5 | 1, 4 | wceq 1475 | 1 wff ℂHil = (Ban ∩ ℂPreHil) |
Colors of variables: wff setvar class |
This definition is referenced by: ishl 22966 |
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