Biconditional Introduction/Proof Rule/Tableau Form

Proof Rule

Let $\phi \implies \psi$ and $\psi \implies \phi$ be two conditional statements involving the two well-formed 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 $\iff \II$

Also denoted as

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