How is it possible to draw any meaningful statements in mathematics from vacuous truths? The material implication and its proof that the empty subset is a subset of every set is the classic example. Now I understand that $P$ does not cause $Q$ to be true and I understand why false antecedents still allow the conditional to be true. 
However, what I don't understand is why we are able to conclude that the empty set is a subset of every set from the material implication since it is vacuously true? Is this just a consequence from the system of formal logic or is it because the empty set is a very special case and that we are allowed to draw a meaningful statement? Or is it both?

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