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  "body": "\n## Summary\n\nA formula is in prenex normal form when all its quantifiers stand at the front, followed by a part without quantifiers.\nIn classical first-order logic every formula is equivalent to a formula in prenex normal form.\nThe string of quantifiers in front measures the logical complexity of the formula, as in the [[arithmetical hierarchy|7CVJCQKY41]].\nPrenex form is also the first step towards [[Skolem normal form|GCPQGMJYEV]].\n\n## Explanations\n\n### L1 human\n\nThe formula $\\forall x \\, \\exists y \\, (x \u003c y \\land y \u003c x + 2)$ has all its quantifiers at the start, so it is in prenex form.\nThe formula $(\\forall x \\, P(x)) \\to Q(c)$ is not, because the quantifier sits inside the implication.\nIt can be rewritten as $\\exists x \\, (P(x) \\to Q(c))$, which means the same thing and is in prenex form.\nPulling quantifiers to the front like this is always possible in classical logic.\n",
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