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Metamath Proof Explorer

Theorem phnvi

Description: Every complex inner product space is a normed complex vector space. (Contributed by NM, 20-Nov-2007) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	phnvi.1	$⊢ U \in {CPreHil}_{OLD}$
	Assertion	phnvi	$⊢ U \in NrmCVec$

Step	Hyp	Ref	Expression
1		phnvi.1	$⊢ U \in {CPreHil}_{OLD}$
2		phnv	$⊢ U \in {CPreHil}_{OLD} \to U \in NrmCVec$
3	1 2	ax-mp	$⊢ U \in NrmCVec$