Law of Identity/Formulation 1/Proof 1

Theorem

$p \vdash p$


Proof

By the tableau method of natural deduction:

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

$\blacksquare$


This is the shortest tableau proof possible.


Sources

  • 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $5$ Further Proofs: Résumé of Rules: Theorem $29$
  • 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.2.1$: Rules for natural deduction
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