Rule of Exportation

Context
Natural deduction.

Definition

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

Proof
These are proved by the tableau method:

$$\left ({p \land q}\right) \Longrightarrow r \vdash p \Longrightarrow \left ({q \Longrightarrow r}\right)$$:

$$p \Longrightarrow \left ({q \Longrightarrow r}\right) \vdash \left ({p \land q}\right) \Longrightarrow r $$: