Indirect Proof

Theorem
Let $P$ be a proposition whose truth value is to be proved (either true or false).

There are two aspects to this:

Reductio ad Absurdum
Thus a reductio ad absurdum argument for the truth of $P$ is a valid argument which takes as a premise the negation of $P$, and from it deduces a contradiction:

Proof by Contradiction
Thus a proof by contradiction argument for the falsehood of $P$ is a valid argument which takes $P$ as a premise, and from it directly deduces a contradiction:

Proof
For proofs, see:


 * Reductio ad Absurdum/Sequent Form
 * Proof by Contradiction/Sequent Form