Rule of Exportation

Context
Natural deduction.

Definition

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

Proof
These are proved by the tableau method:

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

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