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Metamath Proof Explorer

Theorem spansnchi

Description: The span of a singleton in Hilbert space is a closed subspace. (Contributed by NM, 3-Jun-2004) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	spansnch.1	$⊢ A \in ℋ$
	Assertion	spansnchi	$⊢ span (\{A\}) \in C_{ℋ}$

Step	Hyp	Ref	Expression
1		spansnch.1	$⊢ A \in ℋ$
2		spansnch	$⊢ A \in ℋ \to span (\{A\}) \in C_{ℋ}$
3	1 2	ax-mp	$⊢ span (\{A\}) \in C_{ℋ}$