Rule of Implication/Proof Rule/Tableau Form

Proof Rule

Let $\phi$ and $\psi$ be two well-formed formulas in a tableau proof.

The Rule of Implication is invoked for $\phi$ and $\psi$ in the following manner:

			Pool:					The pooled assumptions of $\psi$
			Formula:					$\phi \implies \psi$
			Description:					Rule of Implication
			Depends on:					The series of lines from where the assumption $\phi$ was made to where $\psi$ was deduced
			Discharged Assumptions:					The assumption $\phi$ is discharged
			Abbreviation:					$\text{CP}$ or $\implies \II$

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $2$ Conditionals and Negation