Negation introduction
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 it's complement, then the antecedent is a contradiction" [1]
This can be written as: (P → Q) ∧ (P → ¬Q) ↔ ¬P
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.