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Metamath Proof Explorer

Theorem h0elsh

Description: The zero subspace is a subspace of Hilbert space. (Contributed by NM, 2-Jun-2004) (New usage is discouraged.)

Ref Expression
Assertion h0elsh 0ℋ ∈ Sℋ

Proof

Step Hyp Ref Expression
1 h0elch ⊢ 0ℋ ∈ Cℋ
2 1 chshii ⊢ 0ℋ ∈ Sℋ