Theorem oc0

Description: The zero vector belongs to an orthogonal complement of a Hilbert subspace. (Contributed by NM, 11-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Assertion	oc0	|- ( H e. SH -> 0h e. ( _|_ ` H ) )

Proof

Step	Hyp	Ref	Expression
1		shocsh	|- ( H e. SH -> ( _|_ ` H ) e. SH )
2		sh0	|- ( ( _|_ ` H ) e. SH -> 0h e. ( _|_ ` H ) )
3	1 2	syl	|- ( H e. SH -> 0h e. ( _|_ ` H ) )