Definition:Existential Quantifier/Unique/Also denoted as

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The symbol $\exists_1$ is also found for the same concept, being an instance of the exact existential quantifier $\exists_n$.

Some sources, for example 1972: Patrick Suppes: Axiomatic Set Theory, use $\operatorname E !$, which is idiosyncratic, considering the use in the same source of $\exists$ for the general existential quantifier.