User:Lord Farin/Tableau Proof Rules/Conjunction

Conjunction

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

Line		Pool	Formula	Rule	Depends upon	Notes
$i$		$I$	$p$	?	?
$j$		$J$	$q$	?	?
$k$		$I,J$	$p \land q$	$\land \mathcal I$	$i,j$
$l$		$I,J$	$q \land p$	$\land \mathcal I$	$i,j$

Wiki code

|-
| align="right" | $k$ ||
| align="right" | $I,J$
| $p \land q$
| [[Axiom:Rule of Conjunction|$\land \mathcal I$]]
| $i,j$
|-
| align="right" | $l$ ||
| align="right" | $I,J$
| $q \land p$
| [[Axiom:Rule of Conjunction|$\land \mathcal I$]]
| $i,j$