Theorem chelii

Description: A member of a closed subspace of a Hilbert space is a vector. (Contributed by NM, 6-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	chssi.1	|- H e. CH
	cheli.1	|- A e. H
Assertion	chelii	|- A e. ~H

Proof

Step	Hyp	Ref	Expression
1		chssi.1	|- H e. CH
2		cheli.1	|- A e. H
3	1	chssii	|- H C_ ~H
4	3 2	sselii	|- A e. ~H