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Metamath Proof Explorer

Theorem chshii

Description: A closed subspace is a subspace. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	chshi.1	$⊢ H \in C_{ℋ}$
	Assertion	chshii	$⊢ H \in S_{ℋ}$

Step	Hyp	Ref	Expression
1		chshi.1	$⊢ H \in C_{ℋ}$
2		chsh	$⊢ H \in C_{ℋ} \to H \in S_{ℋ}$
3	1 2	ax-mp	$⊢ H \in S_{ℋ}$