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Definition df-hl 22808
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.)
Assertion
Ref Expression
df-hl ℂHil = (Ban ∩ ℂPreHil)

Detailed syntax breakdown of Definition df-hl
StepHypRef Expression
1 chl 22805 . 2 class ℂHil
2 cbn 22804 . . 3 class Ban
3 ccph 22647 . . 3 class ℂPreHil
42, 3cin 3443 . 2 class (Ban ∩ ℂPreHil)
51, 4wceq 1474 1 wff ℂHil = (Ban ∩ ℂPreHil)
Colors of variables: wff setvar class
This definition is referenced by:  ishl  22832
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