Finding a logical formula (wff) for an englsh expression

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Homework Statement



Suppose P(x) is a statement with a free variable x. Find a formula, using logical symbols, that means "there are exactly two values of x for which P(x) is true."


Homework Equations





The Attempt at a Solution




(∃x)(∃y)(∀z)(P(x) ∧ P(y) ∧ P(z) → ( x=z ∨ y=z) ∧ x≠y)

Is this valid?
 

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