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*Proposition:* For all formulas `A` and `B`, we have

A=>Biff ~ A\/BA=>Biff ~ B=> ~A~( A=>B)iff A/\ ~B.

*Implication can thus be defined by negation and disjunction.*

*Proposition:* Implication is not associative.

*Proof:* by construction of a counterexample:

- Meaning of F => (F => F) is
*true*. - Meaning of (F => F) => F is
*false*.

Author: Wolfgang Schreiner

Last Modification: October 6, 1999