User:Lord Farin/Tableau Proof Rules/Not-Elimination

Principle of Non-Contradiction

Given $p, \neg q$, we have contradiction ($\bot$).

Line		Pool	Formula	Rule	Depends upon	Notes
$i$		$I$	$p$	?	?
$j$		$J$	$\neg p$	?	?
$k$		$I,J$	$\bot$	Principle of Non-Contradiction: $\neg \mathcal E$	$i,j$

Wiki code

|-
| align="right" | $k$ ||
| align="right" | $I,J$
| $\bot$
| [[Principle of Non-Contradiction|Principle of Non-Contradiction: $\neg \mathcal E$]]
| $i,j$