Every torsion-free group is a subgroup of a simple torsion-free group

Statement
Suppose $$G$$ is a fact about::torsion-free group: in other words, no non-identity element of $$G$$ has finite order. Then, there exists a fact about::simple torsion-free group $$L$$ containing $$G$$.

Facts used

 * 1) uses::Every torsion-free group is a subgroup of a torsion-free group with two conjugacy classes

Proof
The proof follows directly from fact (1), and the observation that a group with two conjugacy classes is simple.