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  "body": "\n## Statement\n\nIn type theory, a different kind of statement is known as the axiom of choice. This form begins with two types, σ and τ, and a relation *R* between objects of type σ and objects of type τ. The axiom of choice states that if for each *x* of type σ there exists a *y* of type τ such that *R*(*x*,*y*), then there is a function *f* from objects of type σ to objects of type τ such that *R*(*x*,*f*(*x*)) holds for all *x* of type σ:\n\n$$(\\forall x^\\sigma)(\\exists y^\\tau) R(x,y) \\to (\\exists f^{\\sigma \\to \\tau})(\\forall x^\\sigma) R(x,f(x)).$$\n\nUnlike in set theory, the axiom of choice in type theory is typically stated as an axiom scheme, in which *R* varies over all formulas or over all formulas of a particular logical form.\n",
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