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 e. ~H
Assertion	spansnchi	|- ( span ` { A } ) e. CH

Proof

Step	Hyp	Ref	Expression
1		spansnch.1	|- A e. ~H
2		spansnch	|- ( A e. ~H -> ( span ` { A } ) e. CH )
3	1 2	ax-mp	|- ( span ` { A } ) e. CH