Proof by Contradiction/Variant 3/Formulation 2/Proof 2

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$\vdash \paren {p \implies \neg p} \implies \neg p$


This proof is derived in the context of the following proof system: Instance 2 of the Hilbert-style systems.

By the tableau method:

$\vdash \paren {p \implies \neg p} \implies \neg p$
Line Pool Formula Rule Depends upon Notes
1 $\paren {p \lor p} \implies p$ Axiom $\text A 1$
2 $\paren {\neg p \lor \neg p} \implies \neg p$ Rule $\text {RST} 1$ 1 $\neg p \, / \, p$
3 $\paren {p \implies \neg p} \implies \neg p$ Rule $\text {RST} 2 \, (2)$ 2