11. We fix some axiomatization of the predicate calculus : logical axioms and rules of inference . 12. The concepts described in articles in this category may be also expressed as rules of inference . 13. First-order logic requires at least one additional rule of inference in order to obtain completeness. 14. Axioms are usually regarded as starting points for applying rules of inference and generating a set of conclusions. 15. In other formal proof systems, the deduction theorem is sometimes taken as a primitive rule of inference . 16. Mathematics deals with precise formal definitions and rules of inference and the theorems that can be so derived. 17. As of March 5, there are several such cases in the : Category : Rules of inference . 18. For example, one common rule of inference is the "'rule of substitution " '. 19. A theorem is a statement that can be derived from those axioms by application of these rules of inference . 20. This rule is equivalent to the rule of inference known as modus ponens, except it is going backwards.
