Rule of Simplification/Proof Rule/Tableau Form
Proof Rule
Let $\phi \land \psi$ be a well-formed 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 $\land \EE_1$ |
- 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 $\land \EE_2$ |
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $3$ Conjunction and Disjunction