Torsion-free abelian group axiom scheme ($\forall x(nx=0\to x=0),n\ge 1$)

For an abelian group, the scheme $\forall x(nx=0\to x=0)$ for every positive integer $n$ expresses absence of nonzero elements of finite order. Each fixed $n$ gives one sentence, while the entire scheme expresses the torsion-free abelian group property.