Peirce's Law/Strong Form/Formulation 1
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Theorem
- $\paren {\paren {p \implies q} \implies p} \dashv \vdash p$
Proof
We apply the Method of Truth Tables.
As can be seen by inspection, the truth values under the main connectives match for all boolean interpretations.
$\begin{array}{|ccccc||c|}\hline ((p & \implies & q) & \implies & p) & p \\ \hline \F & \T & \F & \F & \F & \F \\ \F & \T & \T & \F & \F & \F \\ \T & \F & \F & \T & \T & \T \\ \T & \T & \T & \T & \T & \T \\ \hline \end{array}$
$\blacksquare$
Source of Name
This entry was named for Charles Sanders Peirce.