Theorem atcv0

Description: An atom covers the zero subspace. (Contributed by NM, 26-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	atcv0	⊢ ( 𝐴 ∈ HAtoms → 0ℋ ⋖ℋ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ela	⊢ ( 𝐴 ∈ HAtoms ↔ ( 𝐴 ∈ Cℋ ∧ 0ℋ ⋖ℋ 𝐴 ) )
2	1	simprbi	⊢ ( 𝐴 ∈ HAtoms → 0ℋ ⋖ℋ 𝐴 )