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- P <-> Q <=> (P → Q) ^ (Q → R)

Equivalence uses the definition of the biconditional. Claiming that ‘`P if and only if Q`’ is exactly the same as claiming ‘`if P then Q`’ and ‘`if Q then P`’. Equivalence is the only rule that works with biconditionals explicitly, and is thus used any time a biconditional is seen.