Rule of Exportation

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Theorem

Formulation 1

$\left ({p \land q}\right) \implies r \dashv \vdash p \implies \left ({q \implies r}\right)$


Formulation 2

$\vdash \paren {\paren {p \land q} \implies r} \iff \paren {p \implies \paren {q \implies r} }$


Also known as

This rule is also known as the rule of shunting.


Sources