Construction Rules

    ØØA      Ø(A Ú B)     Ø(A ® B)    Ø(A Ù B)    Ø(A « B)

      |           |            |          /   \        /  \

      A           ØA           A        ØA    ØB     A    ØA

                  ØB          ØB                    ØB     B

    Ø("x)A      Ø($x)A

        |           |

     ($x)ØA      ("x)ØA

    (A Ù B)     (A Ú B)     (A ® B)    (A « B)

       |          /  \        /  \        /  \

       A         A    B     ØA    B      A   ØA

       B                                 B   ØB

    ("x)A(x)    This rule is known as Universal Instantiation (UI)

       |       

      A(a)       a is any constant - usually one that has already appeared

    ($x)A(x)    Existential Instantiation (EI)

       |       

      A(a)       a is any constant that has NOT already appeared in that branch

    N.B. Except for UI, no rule can be applied to a wff more than once

    Closure Rule

    When a wff and its negation occur in a branch, close that branch.

        A

       ...

       ØA

        X