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  "body": "\n## Summary\n\nPredicate logic extends [[propositional logic|09K9MWD2QQ]] with variables for objects, [[predicates|0T3DPBG981]] and quantifiers.\nIts formulas can say \"for all $x$\" with the [[universal quantifier|0B88PQTJ66]] and \"there exists $x$\" with the [[existential quantifier|0JW2FHW7G3]].\nIn first-order logic, the quantifiers range over objects, not over sets of objects or predicates.\n\n## Remarks\n\nOther names are first-order logic and predicate calculus.\nAn example of a formula is $\\forall x \\, \\exists y \\, (y \u003e x)$.\nMost of mathematics can be written in first-order logic with the axioms of [[Zermelo–Fraenkel set theory|0HE5WDQ9FJ]].\n\n## Explanations\n\n### L1 human\n\nPropositional logic cannot say \"every number has a larger number\".\nPredicate logic can: it has variables such as $x$ and $y$, and words such as \"for all\" and \"there exists\".\nThis is the logic of most mathematical statements.\n",
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