The law of infinite conjunction (Quine's name, see Methods of logic, rev. ed., Holt & Co., New York, p. 254) says that a set of truthfunctional formulas is satisfiable provided every finite subset is. We give a proof of the law which uses some properties of the perfect disjunctive normal form.

Any satisfiable formula can be written as a disjunction of conjunctions of literals (a literal is a statement-letter or the negation of one) in which a statement-letter which occurs in any conjunction occurs exactly once in each; a literal by itself counts as a conjunction and a conjunction by itself as a disjunction.