Rule of Simplification/Sequent Form/Formulation 1/Proof

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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 $q$.

$\blacksquare$