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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 ∈ 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