| 1. | The substitution rule demonstrates several common aspects of rules of inference.
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| 2. | The closed under application of certain procedures called rules of inference.
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| 3. | Rules of inference must be distinguished from axioms of a theory.
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| 4. | Since formal proofs in proof theory are purely rules of inference.
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| 5. | Typically, a rule of inference preserves truth, a semantic property.
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| 6. | Rules of inference are often formulated as schemata employing metavariables.
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| 7. | It is very closely related to the rule of inference modus tollens.
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| 8. | In argument form and a rule of inference.
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| 9. | First-order predicate logic uses rules of inference to deal with logical quantifiers.
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| 10. | See material implication ( rule of inference ).
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