Law of Identity/Formulation 1

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Every proposition entails itself:

$p \vdash p$

Proof 1

By the tableau method of natural deduction:

$p \vdash p$
Line Pool Formula Rule Depends upon Notes
1 1 $p$ Premise (None)


This is the shortest tableau proof possible.

Proof by Truth Table

We apply the Method of Truth Tables (trivially) to the proposition.

$\begin{array}{|c|c|} \hline p & p \\ \hline \F & \F \\ \T & \T \\ \hline \end{array}$