Definition:Corresponding Conditional

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

It can be expressed as a theorem as follows:

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

This is known as the sequent's corresponding conditional.

This is proved in the Extended Rule of Implication.