Theorem ch0

Description: The zero vector belongs to any closed subspace of a Hilbert space. (Contributed by NM, 24-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Assertion	ch0	⊢ ( 𝐻 ∈ Cℋ → 0ℎ ∈ 𝐻 )

Proof

Step	Hyp	Ref	Expression
1		chsh	⊢ ( 𝐻 ∈ Cℋ → 𝐻 ∈ Sℋ )
2		sh0	⊢ ( 𝐻 ∈ Sℋ → 0ℎ ∈ 𝐻 )
3	1 2	syl	⊢ ( 𝐻 ∈ Cℋ → 0ℎ ∈ 𝐻 )