Rule of Addition/Proof Rule/Tableau Form

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Proof Rule

Let $\phi$ and $\psi$ be two propositional formulas.

The Rule of Addition is invoked in a tableau proof for $\phi$ or $\psi$ in either of the two forms:

Form 1

Let $\phi$ be a propositional formula in a tableau proof.

 Pool: The pooled assumptions of $\phi$ Formula: $\phi \lor \psi$ Description: Rule of Addition Depends on: The line containing $\phi$ Abbreviation: $\operatorname {Add}_1$ or $\lor \mathcal I_1$

Form 2

Let $\psi$ be a propositional formula in a tableau proof.

 Pool: The pooled assumptions of $\psi$ Formula: $\phi \lor \psi$ Description: Rule of Addition Depends on: The line containing $\psi$ Abbreviation: $\operatorname {Add}_2$ or $\lor \mathcal I_2$