Self-Distributive Law for Conditional/Forward Implication/Formulation 2/Proof 2

Proof
We apply the Method of Truth Tables.

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

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