Subvariety of variety of groups containing no nontrivial perfect groups contains only solvable groups

First version
Suppose $$\mathcal{V}$$ is a subvariety of the variety of groups such that $$\mathcal{V}$$ does not contain any nontrivial perfect group. In other words, for every nontrivial group in $$\mathcal{V}$$, the derived subgroup of that group is a proper subgroup of it.

Then, the following are true:


 * Every member of $$\mathcal{V}$$ is a solvable group.
 * Further, there is a common finite bound on the derived length of all members of $$\mathcal{V}$$. In other words, $$\mathcal{V}$$ is a subvariety of a variety of solvable groups with a fixed bound on the derived length.

Second version
Suppose $$\mathcal{V}$$ is a subvariety of the variety of groups that contains a non-solvable group. Then, it contains a nontrivial perfect group.

Note that this is equivalent to the first version by simple logic, without any use of group theory.

Analogues in other algebraic structures

 * Subvariety of variety of Lie rings containing no nontrivial perfect Lie rings contains only solvable Lie rings (the proof is exactly analogous)