Biconditional Introduction

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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.

Proof Rule

If we can conclude both $\phi \implies \psi$ and $\psi \implies \phi$, then we may infer $\phi \iff \psi$.

Sequent Form

$p \implies q, q \implies p \vdash p \iff q$

Also known as

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

Also see