A formula of the predicate calculus is in prenex normal form if it is written as a string of quantifiers (referred to as the prefix) followed by a quantifier-free part (referred to as the matrix).
Every formula in classical logic is equivalent to a formula in prenex normal form. For example, if, and are quantifier-free formulas with the free variables shown then
is in prenex normal form with matrix, while
is logically equivalent but not in prenex normal form.
Read more about Prenex Normal Form: Conversion To Prenex Form, Use of Prenex Form
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