Tautology/Examples/(((not p) implies q) implies (((not p) implies (not q)) implies p))

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

is a tautology.

Proof
Proof by truth table:

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

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