User:Lord Farin/Tableau Proof Rules/Simplification

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Simplification

Given $p \land q$, we have also $p$ and $q$.

Line Pool Formula Rule Depends upon Notes
$i$ $I$ $p \land q$ ? ?
$j$ $I$ $p$ Rule of Simplification: $\land \mathcal E_1$ $i$
$k$ $I$ $q$ Rule of Simplification: $\land \mathcal E_2$ $i$

Wiki code

|-
| align="right" | $j$ ||
| align="right" | $I$
| $p$
| [[Rule of Simplification|Rule of Simplification: $\land \mathcal E_1$]]
| $i$
|-
| align="right" | $k$ ||
| align="right" | $I$
| $q$
| [[Rule of Simplification|Rule of Simplification: $\land \mathcal E_2$]]
| $i$