A rule of inference is admissible with respect to a logical system in case: In logic, especially in mathematical logic, a rule of inference is a scheme for constructing valid inferences. ...
If the rule belongs to the system, every theorem that can be proven making use of the rule can be proven without making use of it;
If the rule doesn't belong to the system, then it is admissible in the system obtained by adding the rule to the system.
See the section in the article on rules of inference for more discussion. In logic, especially in mathematical logic, a rule of inference is a scheme for constructing valid inferences. ...
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Prominent examples of rules of inference in propositional logic are the rules of modus ponens and modus tollens.
Rules of inference must be distinguished from axioms of a theory, which are assertions that are assumed to be true without proof.
Rules of inference play a vital role in the specification of logical calculi as they are considered in proof theory, such as the sequent calculus and natural deduction.
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