Definition df-hlo 27742

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.)

Assertion

Ref	Expression
df-hlo	⊢ CHilOLD = (CBan ∩ CPreHilOLD)

Detailed syntax breakdown of Definition df-hlo

Step	Hyp	Ref	Expression
1		chlo 27741	. 2 class CHilOLD
2		ccbn 27718	. . 3 class CBan
3		ccphlo 27667	. . 3 class CPreHilOLD
4	2, 3	cin 3573	. 2 class (CBan ∩ CPreHilOLD)
5	1, 4	wceq 1483	1 wff CHilOLD = (CBan ∩ CPreHilOLD)

This definition is referenced by:  ishlo  27743