Proof by Contradiction/Explanation

Proof Rule
Proof by Contradiction can be expressed in natural language as follows:

If we know that by making an assumption $\phi$ we can deduce a contradiction, then it must be the case that $\phi$ cannot be true.

Thus it provides a means of introducing a negation into a sequent.

This type of proof is rejected by the intuitionistic school, as it depends on the Law of Excluded Middle.