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