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This article is about rules of inference in logic systems. There are also admissible decision rules in decision theory.
A rule of inference is admissible with respect to a logical system in case:
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.
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