Theorem shelii

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

	Ref	Expression
Hypotheses	shssi.1	|- H e. SH
	sheli.1	|- A e. H
Assertion	shelii	|- A e. ~H

Proof

Step	Hyp	Ref	Expression
1		shssi.1	|- H e. SH
2		sheli.1	|- A e. H
3	1	shssii	|- H C_ ~H
4	3 2	sselii	|- A e. ~H