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 ∈ Cℋ
Assertion	chshii	⊢ 𝐻 ∈ Sℋ

Proof

Step	Hyp	Ref	Expression
1		chshi.1	⊢ 𝐻 ∈ Cℋ
2		chsh	⊢ ( 𝐻 ∈ Cℋ → 𝐻 ∈ Sℋ )
3	1 2	ax-mp	⊢ 𝐻 ∈ Sℋ