Theorem shocsh

Description: The orthogonal complement of a subspace is a subspace. Part of Remark 3.12 of Beran p. 107. (Contributed by NM, 10-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Assertion	shocsh	|- ( A e. SH -> ( _|_ ` A ) e. SH )

Proof

Step	Hyp	Ref	Expression
1		shss	|- ( A e. SH -> A C_ ~H )
2		ocsh	|- ( A C_ ~H -> ( _|_ ` A ) e. SH )
3	1 2	syl	|- ( A e. SH -> ( _|_ ` A ) e. SH )