Question about simple Leibniz algebra $L$ and the simplicity of a quotient of $L$

Question

I want to proof:

"Let $(L,[\cdot,\cdot])$ be a (right or left) Leibniz algebra. If $L$ is a simple then $L/I$ is a simple Lie algebra, being $I$ the ideal generated by the products $[x,x]$, with $x \in L$".

Thanks in advance!