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Wikipedia definition
1. Existence theoremIn mathematics, an existence theorem is a theorem with a statement beginning 'there exist(s) .. ', or more generally 'for all x, y, ... there exist(s) ...'. That is, in more formal terms of symbolic logic, it is a theorem with a statement involving the existential quantifier. Many such theorems will not do so explicitly, as usually stated in standard mathematical language. For example, the statement that the sine function is continuous; or any theorem written in big O notation.
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