Converse, inverse, and contrapositive forms show that conditional statements have structure. Nested conditionals add another layer: one implication may appear inside another. These forms occur naturally in program logic, where one condition may be tested only after another condition is satisfied. In this lesson, nested conditionals and program logic will connect the equivalence $(p\land q)\to r$ with the nested form $p\to(q\to r)$.

Let $p$, $q$, and $r$ be primitive statements. Then $$\begin{equation*} (p\land q)\to r\Leftrightarrow p\to(q\to r). \end{equation*}$$