Theorem hlph

Description: Every complex Hilbert space is an inner product space (also called a pre-Hilbert space). (Contributed by NM, 28-Apr-2007) (New usage is discouraged.)

	Ref	Expression
Assertion	hlph	|- ( U e. CHilOLD -> U e. CPreHilOLD )

Proof

Step	Hyp	Ref	Expression
1		ishlo	|- ( U e. CHilOLD <-> ( U e. CBan /\ U e. CPreHilOLD ) )
2	1	simprbi	|- ( U e. CHilOLD -> U e. CPreHilOLD )