Rule of Simplification/Sequent Form/Formulation 1/Form 2/Proof by Truth Table

Theorem

 * $p \land q \vdash q$

Proof
We apply the Method of Truth Tables.

$\begin{array}{|ccc||c|} \hline p & \land & q & q \\ \hline F & F & F & F \\ F & F & T & T \\ T & F & F & F \\ T & T & T & T \\ \hline \end{array}$

As can be seen, when $p \land q$ is true so is $q$.