True Statement is implied by Every Statement/Formulation 2/Proof by Truth Table

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth value under the main connective, the first instance of $\implies$, is $\T$ for each boolean interpretation.

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