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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

Speaker notes:

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