Rule of Simplification/Sequent Form

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Theorem

The Rule of Simplification can be symbolised by the sequents:

Formulation 1

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


Formulation 2

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