$l_{1}$-block basic sequences in Banach spaces with an unconditional basis

Let $$X$$ be a Banach space with an unconditional basis $$(x_{n})_{n}$$.

Question. If $$X$$ contains a subspace isomorphic to $$l_{1}$$, does $$(x_{n})_{n}$$ admit a block basic sequence equivalent to the unit vector basis of $$l_{1}$$ ?

I do not know whether the question has already existed as a known result. But a self-contained proof is preferred.

Thank you.