Editing If and only if (section)

===Proofs===
In most [[logical system]]s, one [[Proof theory|proves]] a statement of the form "P iff Q" by proving either "if P, then Q" and "if Q, then P", or "if P, then Q" and "if not-P, then not-Q". Proving these pairs of statements sometimes leads to a more natural proof, since there are not obvious conditions in which one would infer a biconditional directly. An alternative is to prove the [[disjunction]] "(P and Q) or (not-P and not-Q)", which itself can be inferred directly from either of its disjuncts—that is, because "iff" is [[truth-function]]al, "P iff Q" follows if P and Q have been shown to be both true, or both false.