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Proofs

  • A proof of a conclusion from a set of premises is a sequence of sentences terminating in the conclusion in which each item is either

  1. a premise,

  2. an instance of an axiom schema, or

  3. the result of applying a rule of inference to earlier items in sequence

  • Example:

    1. p → q

    		Premise

    2. q → r

    		Premise

    3. ( q → r ) → ( p → ( q → r ))

    		II

    4. p → ( q → r )

    		MP : 3,2

    5. ( p → ( q → r )) → (( p → q ) →( p → r ))

    		ID

    6. ( p → q ) → ( p → r )

    		MP : 5,4

    7. p → r

    		MP : 6,1

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