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Metamath Proof Explorer

Theorem shocss

Description: An orthogonal complement is a subset of Hilbert space. (Contributed by NM, 11-Oct-1999) (New usage is discouraged.)

		Ref	Expression
	Assertion	shocss	$⊢ A \in S_{ℋ} \to ⊥ (A) \subseteq ℋ$

Step	Hyp	Ref	Expression
1		shss	$⊢ A \in S_{ℋ} \to A \subseteq ℋ$
2		ocss	$⊢ A \subseteq ℋ \to ⊥ (A) \subseteq ℋ$
3	1 2	syl	$⊢ A \in S_{ℋ} \to ⊥ (A) \subseteq ℋ$