Definition:Corresponding Conditional

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Let $p_1, p_2, p_3, \ldots, p_n \vdash q$ be a sequent of propositional logic.

It can be expressed as a theorem as follows:

$\vdash p_1 \implies \left({p_2 \implies \left({p_3 \implies \left({\ldots \implies \left({p_n \implies q}\right) \ldots }\right)}\right)}\right)$

This is known as the sequent's corresponding conditional.

This is proved in the Extended Rule of Implication.