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mathoverflow_21003

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Is there any polynomial $f(x, y) \in \mathbb{Q}[x, y]$ such that $f : \mathbb{Q} \times \mathbb{Q} \rightarrow \mathbb{Q}$ is a bijection?

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Lean 4 Statement 
theorem mathoverflow_21003 :
    answer(sorry) ↔ ∃ f : MvPolynomial (Fin 2) ℚ, Function.Bijective fun x ↦ f.eval x
ID: Mathoverflow__21003__mathoverflow_21003
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