# Rule of Simplification/Proof Rule/Tableau Form

## Proof Rule

Let $\phi \land \psi$ be a propositional formula in a tableau proof whose main connective is the conjunction operator.

The Rule of Simplification is invoked for $\phi \land \psi$ in either of the two forms:

Form 1
 Pool: The pooled assumptions of $\phi \land \psi$ Formula: $\phi$ Description: Rule of Simplification Depends on: The line containing $\phi \land \psi$ Abbreviation: $\operatorname {Simp}_1$ or $\land \mathcal E_1$

Form 2
 Pool: The pooled assumptions of $\phi \land \psi$ Formula: $\psi$ Description: Rule of Simplification Depends on: The line containing $\phi \land \psi$ Abbreviation: $\operatorname {Simp}_2$ or $\land \mathcal E_2$