Pqq~pvq~TTFTTFTTFTFFFFTTPp~qq~p~vq~TFTFFTFFTTFTTFTFTFTTPqq ⟹ pTTTTFTFTFFFTPqrp ⟹ q(~p ⟹ q)(~p ⟹ q) ⟹ rTTTTFTTTFTFTTFTFTTTFFFTFFTTTFTFTFTFTFFTTFTFFFTFT\begin{matrix} P & q&\tilde q &pv\tilde q\\ T&T&F&T\\ T&F&T&T\\ F&T&F&F\\ F&F&T&T\\ \end{matrix}\\ \begin{matrix} P & \tilde p& q&\tilde q &\tilde pv\tilde q\\ T&F&T&F&F\\ T&F&F&T&T\\ F&T&T&F&T\\ F&T&F&T&T\\ \end{matrix}\\ \begin{matrix} P & q&q\implies p\\ T&T&T\\ T&F&T\\ F&T&F\\ F&F&T\\ \end{matrix}\\ \begin{matrix} P & q&r&p\implies q&\tilde( p \implies q)&\tilde(p\implies q)\implies r\\ T&T&T&T&F&T\\ T&T&F&T&F&T\\ T&F&T&F&T&T\\ T&F&F&F&T&F\\ F&T&T&T&F&T\\ F&T&F&T&F&T\\ F&F&T&T&F&T\\ F&F&F&T&F&T\\ \end{matrix}\\PTTFFqTFTFq~FTFTpvq~TTFTPTTFFp~FFTTqTFTFq~FTFTp~vq~FTTTPTTFFqTFTFq⟹pTTFTPTTTTFFFFqTTFFTTFFrTFTFTFTFp⟹qTTFFTTTT(~p⟹q)FFTTFFFF(~p⟹q)⟹rTTTFTTTT
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