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The LaTeX command for exists (∃) is \exists — there exists / existential quantifier.
\existsWrite \exists inside math mode — that is, between $…$ for inline math or in a \[ … \] / equation block for display math. It is part of core LaTeX math, so no extra package is required.
$p \exists q$Prefer to see it live? Paste it into the LaTeX preview and it renders as you type — no compiler, no signup.
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Use \exists in math mode — it needs no extra package. For example, $p \exists q$.
None — \exists is built into LaTeX's math mode, so no extra package is required.