Rule of Simplification/Sequent Form/Formulation 2/Proof 1/Form 1

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Theorem

$\vdash p \land q \implies p$


Proof

By the tableau method of natural deduction:

$\vdash p \land q \implies p$
Line Pool Formula Rule Depends upon Notes
1 1 $p \land q$ Assumption (None)
2 1 $p$ Rule of Simplification: $\land \EE_1$ 1
3 $p \land q \implies p$ Rule of Implication: $\implies \II$ 1 – 2 Assumption 1 has been discharged

$\blacksquare$


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