Each of these patterns is an "axiom schema", a rule for generating an infinite number of axioms. For example, if formula_9, formula_10, and formula_11 are propositional variables, then formula_12 and formula_13 are both instances of axiom schema 1, and hence are axioms. It can be shown that with only these three axiom schemata and "modus ponens", one can prove all tautologies of the propositional calculus. It can also be shown that no pair of these schemata is sufficient for proving all tautologies with "modus ponens".