Biconditional Introduction/Proof Rule

Proof Rule
The rule of biconditional introduction is a valid argument in types of logic dealing with conditionals $\implies$ and biconditionals $\iff$.

This includes classical propositional logic and predicate logic, and in particular natural deduction.

As a proof rule it is expressed in the form:
 * If we can conclude both $\phi \implies \psi$ and $\psi \implies \phi$, then we may infer $\phi \iff \psi$.

It can be written:
 * $\ds { {\phi \implies \psi \qquad \psi \implies \phi} \over \phi \iff \psi} \iff_i$

Thus it is used to introduce the biconditional operator into a sequent.

Also see

 * This is a rule of inference of the following proof systems:
 * Definition:Natural Deduction