Negation introduction

In symbolic logic, a valid inference in a system of truth-functional rules. This rule relies on the concept of noncontradiction: A valid argument’s conclusion cannot be false if the premise(s) is (are) true. The negation introduction rule proceeds by assuming a statement at the start of a subproof, from which a contradiction is derived. That contradiction shows the assumption is false. The subproof ends with the introduction of a negation of that assumption.