Modus Ponendo Ponens/Variant 1/Proof by Truth Table

Proof
We apply the Method of Truth Tables.

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

As can be seen by inspection, when $p$ is true, the value of the main connective is also true.