Rule of Conjunction/Sequent Form/Formulation 1/Proof 1

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Theorem

\(\ds p\) \(\) \(\ds \)
\(\ds q\) \(\) \(\ds \)
\(\ds \vdash \ \ \) \(\ds p \land q\) \(\) \(\ds \)


Proof

By the tableau method of natural deduction:

$p, q \vdash p \land q$
Line Pool Formula Rule Depends upon Notes
1 1 $p$ Premise (None)
2 2 $q$ Premise (None)
3 1, 2 $p \land q$ Rule of Conjunction: $\land \II$ 1, 2

$\blacksquare$


Sources