Rule of Simplification/Sequent Form

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Theorem

The Rule of Simplification can be symbolised by the sequents:

Formulation 1

\(\text {(1)}: \quad\) \(\ds p \land q\) \(\) \(\ds \)
\(\ds \vdash \ \ \) \(\ds p\) \(\) \(\ds \)
\(\text {(2)}: \quad\) \(\ds p \land q\) \(\) \(\ds \)
\(\ds \vdash \ \ \) \(\ds q\) \(\) \(\ds \)


Formulation 2

$(1): \quad \vdash p \land q \implies p$
$(2): \quad \vdash p \land q \implies q$