# Negation introduction

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Transformation rules |
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Propositional calculus |

Rules of inference |

Rules of replacement |

Predicate logic |

**Negation introduction** is a rule of inference, or transformation rule, in the field of propositional calculus.

Negation introduction states that if a given antecedent implies both the consequent and its complement, then the antecedent is a contradiction.^{[1]} ^{[2]}

## Formal notation[edit]

This can be written as:

An example of its use would be an attempt to prove two contradictory statements from a single fact. For example, if a person were to state "When the phone rings I get happy" and then later state "When the phone rings I get annoyed", the logical inference which is made from this contradictory information is that the person is making a false statement about the phone ringing.

## References[edit]

**^**Wansing, Heinrich, ed. (1996).*Negation: A Notion in Focus*. Berlin: Walter de Gruyter. ISBN 3110147696.**^**Haegeman, Lilliane (30 Mar 1995).*The Syntax of Negation*. Cambridge: Cambridge University Press. p. 70. ISBN 0521464927.