Rule of Exportation/Forward Implication/Formulation 2/Proof 2

Proof
We apply the Method of Truth Tables to the proposition.

As can be seen by inspection, the truth values under the main connective are true for all boolean interpretations.

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