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 ∈ CHilOLD → 𝑈 ∈ CPreHilOLD )

Proof

Step	Hyp	Ref	Expression
1		ishlo	⊢ ( 𝑈 ∈ CHilOLD ↔ ( 𝑈 ∈ CBan ∧ 𝑈 ∈ CPreHilOLD ) )
2	1	simprbi	⊢ ( 𝑈 ∈ CHilOLD → 𝑈 ∈ CPreHilOLD )