Rule of Simplification/Sequent Form/Formulation 1/Proof

Theorem

 * $(1): \quad p \land q \vdash p$
 * $(2): \quad p \land q \vdash q$

Proof
We apply the Method of Truth Tables.

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

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