| 21. | As before, all rules of inference in finitary logic can be used, together with an additional one:
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| 22. | Having proved these two steps, the rule of inference establishes the statement to be true for all natural numbers.
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| 23. | In mathematics, "'proof by contraposition "'is a rule of inference used in proofs.
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| 24. | Also, notice that contraposition is a method of inference which may require the use of other rules of inference.
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| 25. | A formal system is determined by a formal language and a deductive system ( axioms and rules of inference ).
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| 26. | The goal was to find valid rules of inference and forms of proof to help people find their way in life.
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| 27. | The MI string is akin to a single axiom, and the four transformation rules are akin to rules of inference.
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| 28. | A special case of this, an axiomatic theory, consists of axioms ( or axiom schemata ) and rules of inference.
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| 29. | Typically it also has one or two non-logical rules of inference, such as constructive versions of induction or comprehension.
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| 30. | Popular rules of inference in propositional logic include " modus ponens ", " modus tollens ", and contraposition.
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