Definition df-hl 24406

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 subfield of the field of complex numbers closed under square roots of nonnegative reals. (Contributed by Steve Rodriguez, 28-Apr-2007.)

Assertion

Ref	Expression
df-hl	⊢ ℂHil = (Ban ∩ ℂPreHil)

Detailed syntax breakdown of Definition df-hl

Step	Hyp	Ref	Expression
1		chl 24403	. 2 class ℂHil
2		cbn 24402	. . 3 class Ban
3		ccph 24235	. . 3 class ℂPreHil
4	2, 3	cin 3882	. 2 class (Ban ∩ ℂPreHil)
5	1, 4	wceq 1539	1 wff ℂHil = (Ban ∩ ℂPreHil)

This definition is referenced by:  ishl  24431