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  "body": "\n## Definition\n\nLet $X$ be a set and let $P(x)$ be a [[predicate|0T3DPBG981]] on $X$.\nThe existential quantification of $P$ over $X$ is the proposition $\\exists x \\in X, \\, P(x)$, read \"there exists $x$ in $X$ such that $P(x)$\".\nIt is true when $P(a)$ is true for at least one $a \\in X$, and false otherwise.\n\n## Remarks\n\nWhen $X$ is empty, $\\exists x \\in X, \\, P(x)$ is false for each $P$.\nFor a finite set $X = \\{a_1, \\dots, a_n\\}$, the statement is equivalent to $P(a_1) \\lor \\dots \\lor P(a_n)$.\nThe [[uniqueness quantifier|0N3ADS4CHH]] $\\exists!$ says that exactly one element exists.\n\n## Explanations\n\n### L1 human\n\n\"There is an even prime number\" is $\\exists n \\in \\mathbb{N}, \\, (n \\text{ is even} \\land n \\text{ is prime})$.\nTo prove it, one example is enough: $n = 2$.\n",
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