indirect proof

Machine-translated from the Swedish article

An indirect proof or proof by contradiction is a way of proving a statement by showing that the negation of the statement leads to a self-contradiction. If the statement to be derived is P {\displaystyle \ P} , in an indirect proof one assumes the negation of the theorem, ¬ P {\displaystyle \neg P} . If this assumption together with the given premises leads to a contradiction, then one can, using the above-mentioned rule of inference, conclude that P {\displaystyle \ P} is valid.