Proof by Cases/Proof Rule

Proof Rule
The Rule of Conjunction is a valid deduction sequent in propositional logic.

As a proof rule it is expressed in the form:
 * If we can conclude $\phi \lor \psi$, and:
 * $(1): \quad$ By making the assumption $\phi$, we can conclude $\chi$
 * $(2): \quad$ By making the assumption $\psi$, we can conclude $\chi$
 * then we may infer $\chi$.

The conclusion $\chi$ does not depend upon either assumption $\phi$ or $\psi$.

It can be written:
 * $\displaystyle {\phi \lor \psi \quad \begin{array}{|c|} \hline \phi \\ \vdots \\ \chi \\ \hline \end{array} \quad \begin{array}{|c|} \hline \psi \\ \vdots \\ \chi \\ \hline \end{array} \over \chi} \lor_e$

Also see

 * Rule of Addition

Technical Note
When invoking the Rule of Or-Elimination in a tableau proof, use the OrElimination template:



where:
 * is the number of the line on the tableau proof where the Rule of Or-Elimination is to be invoked
 * is the pool of assumptions (comma-separated list)
 * is the statement of logic that is to be displayed in the Formula column, without the  delimiters
 * is the line of the tableau proof where the disjunction being eliminated is situated
 * is the start line of the block of the tableau proof upon which the demonstration of the first disjunct directly depends
 * is the end line of the block of the tableau proof upon which the demonstration of the first disjunct directly depends
 * is the start line of the block of the tableau proof upon which the demonstration of the second disjunct directly depends
 * is the end line of the block of the tableau proof upon which the demonstration of the second disjunct directly depends