Biconditional Elimination/Proof Rule

Theorem
The rule of biconditional elimination 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 either of the two forms:
 * $(1): \quad$ If we can conclude $\phi \iff \psi$, then we may infer $\phi \implies \psi$.
 * $(2): \quad$ If we can conclude $\phi \iff \psi$, then we may infer $\psi \implies \phi$.

It can be written:
 * $\ds {\phi \iff \psi \over \phi \implies \psi} {\iff}_{e_1} \qquad \text{or} \qquad {\phi \iff \psi \over \psi \implies \phi} {\iff}_{e_2}$

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