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Definition df-hl 23353
Description: Define the class of all subcomplex Hilbert spaces. A subcomplex Hilbert space is a Banach space which is also an inner product space over a quadratically closed subfield of the field of 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 23350 . 2 class ℂHil
2 cbn 23349 . . 3 class Ban
3 ccph 23185 . . 3 class ℂPreHil
42, 3cin 3722 . 2 class (Ban ∩ ℂPreHil)
51, 4wceq 1631 1 wff ℂHil = (Ban ∩ ℂPreHil)
Colors of variables: wff setvar class
This definition is referenced by:  ishl  23377
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