This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem hlnv

Description: Every complex Hilbert space is a normed complex vector space. (Contributed by NM, 17-Mar-2007) (New usage is discouraged.)

		Ref	Expression
	Assertion	hlnv	$⊢ U \in {CHil}_{OLD} \to U \in NrmCVec$

Step	Hyp	Ref	Expression
1		hlobn	$⊢ U \in {CHil}_{OLD} \to U \in CBan$
2		bnnv	$⊢ U \in CBan \to U \in NrmCVec$
3	1 2	syl	$⊢ U \in {CHil}_{OLD} \to U \in NrmCVec$