Tautology/Examples/((not p) implies (q or r)) iff ((not q) implies ((not r) implies p))

Examples of Tautologies
The WFF of propositional logic:
 * $\paren {\paren {\lnot p} \implies \paren {q \lor r} } \iff \paren {\paren {\lnot q} \implies \paren {\paren {\lnot r} \implies p} }$

is a tautology.

Proof
Proof by truth table:

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

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