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Implicative Laws

Proposition: For all formulas A and B, we have

A => B iff ~A \/ B
A => B iff ~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:

Author: Wolfgang Schreiner
Last Modification: October 6, 1999

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