Theorem elatcv0

Description: A Hilbert lattice element is an atom iff it covers the zero subspace. (Contributed by NM, 26-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	elatcv0	⊢ ( 𝐴 ∈ Cℋ → ( 𝐴 ∈ HAtoms ↔ 0ℋ ⋖ℋ 𝐴 ) )

Proof

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