Modus Tollendo Ponens/Variant/Formulation 2/Proof by Truth Table

Theorem

 * $\vdash \left({p \lor q}\right) \iff \left({\neg p \implies q}\right)$

Proof
We apply the Method of Truth Tables.

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

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