Peirce's theorem

Peirce's theorem is a principle in logic stating that if a proposition is true, then knowing it's true confirms the truth of related logical statements. Essentially, it formalizes the idea that the truth of a statement supports the validity of conclusions drawn from it. In formal logic, it demonstrates how certain logical relations remain valid under specific conditions, helping to ensure the consistency and reliability of reasoning processes. This theorem is part of the foundation that underpins logical deduction, ensuring that if the initial assumptions are true, the derived conclusions are also true.