Negation introduction

Formal notation

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.


Step Proposition Derivation
2Material implication
5Conjunction elimination (4)
7Law of noncontradiction
8Disjunctive syllogism (5,6)
10Conjunction elimination (7)
11Idempotency of disjunction


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