Rule of Simplification/Sequent Form

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

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