Definition:Corresponding Conditional

Definition
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:


 * $\vdash p_1 \implies \paren {p_2 \implies \paren {p_3 \implies \paren {\ldots \implies \paren {p_n \implies q} \ldots } } }$

This is known as the sequent's corresponding conditional.

Also see

 * Extended Rule of Implication, where the validity of this construction is proved.