# Law of The Excluded Middle This states that "Either p or non-p" must be true (no third possibility). The variable 'p' is a placeholder for any statement or proposition > something is either prime or not prime Above isn't just repeating this general principle, it's applying it. To get there, it uses the "Rule of Substitution for Sentential Variables." This rule allows you to replace variables (like 'p') with specific statements (like "y is prime" ) within a logical form.