if and only if
Exactly when true
If and only if establishes that two conditions are logically equivalent—each one guarantees the other.
A triangle is equilateral if and only if all its angles are equal: having equal sides means having equal angles, and having equal angles means having equal sides.
The phrase appears in mathematics, logic, and philosophy, often abbreviated as "iff." It's stronger than plain "if," which allows one-way implication.
- negationDenial or cancellation
- sufficiencyState of being enough
- equivalenceState of being equal
- both waysIn two directions
- necessityIndispensable requirement
biconditional · contrapositive · proposition · tautology · boolean · logical · fit · predicate · key · conjunction · proof · formal logic · truth value · match · theorem · hypothesis · conclusion · axiom
if and only ifif
Conditional clause marker
only if · implies · unless · sufficient condition · necessary condition
if and only ifmaybe
Expression of uncertainty
perhaps · possibly · sometimes · coincidentally · occasionally
if and only ifroughly
In approximate terms
approximately · more or less · sort of · vaguely · somewhat