Direct proof starts from the hypothesis and derives the conclusion. Some theorems are easier to prove indirectly. Indirect proof methods for theorems include proof by contraposition and proof by contradiction. These methods are valid because of logical equivalences involving implication and negation. In this lesson, indirect proof methods for theorems are used to prove parity results, product results, square results, and inequalities.

A direct proof of an implication starts from the hypothesis and uses definitions, known results, and logical rules to derive the conclusion. For a theorem of the form $p\to q$, a direct proof assumes $p$ and proves $q$.