Page "Proof by contradiction" Paragraph 31

In the above, P is the proposition we wish to disprove respectively prove ; and S is a set of statements, which are the premises — these could be, for example, the axioms of the theory we are working in, or earlier theorems we can build upon.

We consider P, or the negation of P, in addition to S ; if this leads to a logical contradiction F, then we can conclude that the statements in S lead to the negation of P, or P itself, respectively.