Substitution is replacing the terms in an expression to create a new expression. Substituting 3 for in the expression makes a new expression with meaning . Substituting the terms of a statement makes a new statement. When the original statement is true independently of the values of the terms, the statement created by substitutions is also true. Hence, definitions can be made in symbolic terms and interpreted through substitution: if formula_74 is meant as the definition of formula_75 as the product of with itself, substituting for informs the reader of this statement that formula_76 means . Often it's not known whether the statement is true independently of the values of the terms. And, substitution allows one to derive restrictions on the possible values, or show what conditions the statement holds under. For example, taking the statement , if is substituted with , this implies , which is false, which implies that if then cannot be .