Proof for a corollary from PBW theorem

Question

I need to know how we can prove the following corollary : If $x_1, \ldots, x_n$ is a vector space basis for Lie algebra $L$ then a vector space basis for $U(L)$, $U(L)$ is universal enveloping algebra, is given by all monomials of the form $x_{j1}, x_{j2}, \ldots, x_{jl}$. I want to know how we can investigate the linearly independent of basis like those?