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

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Theorem

$\vdash p \land q \implies q$


Proof

By the tableau method of natural deduction:

$\vdash p \land q \implies q$
Line Pool Formula Rule Depends upon Notes
1 1 $p \land q$ Assumption (None)
2 1 $q$ Rule of Simplification: $\land \EE_2$ 1
3 $p \land q \implies q$ Rule of Implication: $\implies \II$ 1 – 2 Assumption 1 has been discharged

$\blacksquare$