Given some function involving two variables, $\mathit p(x,y)$, is the formula $$\mathit \exists!x\exists yp(x,y)$$ equivalent to $$\mathit\exists y\exists!xp(x,y)$$ I have tried writing out the formal definition for the unique existential quantifier, but I get stuck simplifying the statement when the unique quantifier is first. I have also tried giving $\mathit p(x,y)$ some meaning and talking through it, but I can't decide if they mean the same thing. Any help is appreciated!
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