Theorem shssii

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

	Ref	Expression
Hypothesis	shssi.1	|- H e. SH
Assertion	shssii	|- H C_ ~H

Proof

Step	Hyp	Ref	Expression
1		shssi.1	|- H e. SH
2		shss	|- ( H e. SH -> H C_ ~H )
3	1 2	ax-mp	|- H C_ ~H