The theorem stated below is due to R. Balbes. The present proof is direct; it uses only the following two well-known facts: (i) Let K be a category of algebras, and let free algebras exist in K; then an algebra is projective if and only if it is a retract of a free algebra, (ii) Let F be a free distributive lattice with basis {x i | i ∊ I}; then ∧(x i | i ∊ J 0) ≤ ∨(x i | i ∊ J 1) implies J 0∩J 1≠ϕ. Note that (ii) implies (iii): If for J 0 ⊆ I, a, b ∊ F, ∧(x i | i ∊ J 0)≤a ∨ b, then ∧ (x i | i ∊ J 0)≤ a or b.