A corollary is a statement that follows readily from a previously proven statement or theorem. It often serves as a natural extension or consequence of the original idea, making it easier to understand and apply. In mathematics, corollaries help to simplify complex concepts by providing additional insights or results that are directly related to the main theorem. In logic and philosophy, corollaries can also illustrate the implications of a particular argument or theory. They help clarify how one idea leads to another, reinforcing the connections between different concepts. This makes corollaries valuable tools in both academic and practical applications, such as in mathematics and scientific reasoning.