Evaluating logic statement with quantifier

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P(x)= ( ≠ 1 ∧ ∀, ∈ ℕ ( = → ( = 1 ∨ = ))) , ∀ ∈ ℕ.

What can I say about x if P(x) is true for this statement other than x can be expressed as a product of 1 and its own.

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Well, the predicate $P(x)$ states that $x$ is prime, since a prime $x$ is only divisible by $1$ or itself (if you consider as underlying set the natural numbers).