Go backward to Operational Interpretation
Go up to Top
Go forward to Equivalences
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: