Theorem shssii

Description: A closed subspace of a Hilbert space is a subset of Hilbert space. (Contributed by NM, 6-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypothesis	shssi.1	⊢ 𝐻 ∈ Sℋ
Assertion	shssii	⊢ 𝐻 ⊆ ℋ

Proof

Step	Hyp	Ref	Expression
1		shssi.1	⊢ 𝐻 ∈ Sℋ
2		shss	⊢ ( 𝐻 ∈ Sℋ → 𝐻 ⊆ ℋ )
3	1 2	ax-mp	⊢ 𝐻 ⊆ ℋ