# Biconditional Introduction/Proof Rule/Tableau Form

Let $\phi \implies \psi$ and $\psi \implies \phi$ be two conditional statements involving the two propositional formulas $\phi$ and $\psi$ in a tableau proof.
Biconditional Introduction is invoked for $\phi$ and $\psi$ in the following manner:
 Pool: The pooled assumptions of each of $\phi \implies \psi$ and $\psi \implies \phi$ Formula: $\phi \iff \psi$ Description: Biconditional Introduction Depends on: Both of the lines containing $\phi \implies \psi$ and $\psi \implies \phi$ Abbreviation: $\mathrm {BI}$ or $\iff \mathcal I$
Sources which refer to this rule as the conditional-biconditional rule may as a consequence give the abbreviation $\mathrm {CB}$.