Biconditional Introduction/Proof Rule/Tableau Form

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Proof Rule

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 $\iff \mathcal I$             


Also denoted as

Sources which refer to this rule as the conditional-biconditional rule may as a consequence give the abbreviation $\mathrm {CB}$.