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Metamath Proof Explorer

Theorem shoccl

Description: Closure of complement of Hilbert subspace. Part of Remark 3.12 of Beran p. 107. (Contributed by NM, 13-Oct-1999) (New usage is discouraged.)

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

Proof

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