◀ ▲ ▶Branches / Logic / Lemma: Negation of an Implication
Another important lemma is the way how to negate an implication.
Lemma: Negation of an Implication
The negation of an implication $x\Rightarrow y$ is equivalent to the conjunction of the antecedent $x$ and the negated consequent $\neg y$, formally $$\neg (x\Rightarrow y)\Longleftrightarrow (x \wedge \neg y).$$
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References
Bibliography
 Mendelson Elliott: "Theory and Problems of Boolean Algebra and Switching Circuits", McGrawHill Book Company, 1982