Exercise 20.

Suppose \(P_1, P_2, \ldots, P_n\) and \(Q\) are (possibly molecular) propositional statements. Suppose further that

\(P_1\)
\(P_2\)
\(\vdots\)
\(P_n\)
\(\therefore\) \(Q\)

is a valid deduction rule. Prove that the statement

\begin{equation*} (P_1 \wedge P_2 \wedge \cdots \wedge P_n) \imp Q \end{equation*}

is a tautology.

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