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 $\mathrm {CB}$.