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[itex](\exists!x)P(x)[/itex] is equivalent to [itex](\exists x)P(x)\wedge(\forall y)(\forall z)[P(y)\wedge P(z)\Rightarrow y=z][/itex]

But I don't see why the variable z is necessary. Wouldn't the following also be correct but shorter and easier to understand:

[itex](\exists x)P(x)\wedge(\forall y)(P(y)\Rightarrow y=x)[/itex]

??

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# Unique existence quantifier equivalent to what?

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