Rule of Implication/Sequent Form/Proof by Truth Table

Proof
We apply the Method of Truth Tables.

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

As can be seen by inspection, only when $p$ is true and $q$ is false, then so is $p \implies q$ also false.