# Biconditional Elimination

## 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.

### Proof Rule

$(1): \quad$ 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 $\psi \implies \phi$.

### Sequent Form

 $\text {(1)}: \quad$ $\ds p \iff q$ $\vdash$ $\ds p \implies q$ $\text {(2)}: \quad$ $\ds p \iff q$ $\vdash$ $\ds q \implies p$

## Also known as

Some sources refer to the Biconditional Elimination as the rule of Biconditional-Conditional.