Metamath Proof Explorer


Definition df-hlo

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.)

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

Detailed syntax breakdown

Step Hyp Ref Expression
0 chlo CHilOLD
1 ccbn CBan
2 ccphlo CPreHilOLD
3 1 2 cin ( CBan ∩ CPreHilOLD )
4 0 3 wceq CHilOLD = ( CBan ∩ CPreHilOLD )