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Metamath Proof Explorer

Theorem chsssh

Description: Closed subspaces are subspaces in a Hilbert space. (Contributed by NM, 29-May-1999) (Revised by Mario Carneiro, 23-Dec-2013) (New usage is discouraged.)

		Ref	Expression
	Assertion	chsssh	⊢ C_ℋ ⊆ S_ℋ

Proof

Step	Hyp	Ref	Expression
1		chsh	⊢ ( 𝑥 ∈ C_ℋ → 𝑥 ∈ S_ℋ )
2	1	ssriv	⊢ C_ℋ ⊆ S_ℋ