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<p>theorem for arbitrary formulas of first-order logic, the simpler version shown here, restricted to formulas in <a href="page.php?w=prenex_form">prenex form</a> containing only <a href="page.php?w=existential_quantifier">existential quantifier</a>s, became more popular.</p>

<p><big>Statement</big></p>
<p>Let </p>

<p>
:</p>

<p>be a formula of first-order logic with  quantifier-free,though it may contain additional free variables.This version of Herbrand's theorem states that the above formula is <a href="page.php?w=validity_%28logic%29">valid</a> if</p><p>
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