What process consist of a logical chain of steps that show that a statement must be true?

The process you are describing is known as a proof. In mathematics and logic, a proof is a structured argument that starts with axioms or previously established statements and uses logical reasoning to demonstrate the truth of a particular proposition. Each step in the proof builds on prior statements, ensuring that the conclusion follows logically from the premises. This rigorous approach ensures that the statement is validated within the framework of the given system.