Definition:Corresponding Conditional

Any sequent of natural deduction can be expressed as a theorem.

That is:

$$p_1, p_2, p_3, \ldots, p_n \vdash q$$

means the same thing as:

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

This is proved in the Extended Rule of Implication.