An independent system of identities for a variety of mono-Leibniz algebras

We introduce the notion of a mono-Leibniz algebra generalizing the concept of a Leibniz algebra. Namely, an algebra $A$ over a field $K$, $\operatorname{char}K\ne2$, is mono-Leibniz if its one-generated subalgebras each is a Leibniz algebra. It is proved that a variety $W$ of mono-Leibniz algebras over an infinite field $K$ is defined by an independent system of identities such as
$$ x(xx)=0,\qquad x[(xx)x]=0. $$
Examples of mono-Leibniz algebras are given which show that $W$ is not a Schreier variety.