The Consistency Theorem states that a sentence φ is logically consistent with a sentence ψ if and only if the sentence (φ ∧ ψ) is satisfiable. More generally, a sentence φ is logically consistent with a finite set of sentences {φ₁, ... , φ_n} if and only if the single compound sentence (φ₁ ∧ ... ∧ φ_n ∧ φ) is satisfiable.