Theorem sheli

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
Hypothesis	shssi.1	|- H e. SH
Assertion	sheli	|- ( A e. H -> A e. ~H )

Proof

Step	Hyp	Ref	Expression
1		shssi.1	|- H e. SH
2	1	shssii	|- H C_ ~H
3	2	sseli	|- ( A e. H -> A e. ~H )