Is this really worthy of being pointed out as a corollary??
I misread it, thought that the corollary was about dependance too.
That's true, but not for the reason that you seem to be thinking. Every vector space contains 0, and therefore is a linearly dependent set, but if you remove that point you could have a linearly independent set. For example (and probably the only example), F2 the field of two elements, as a one dimensional vector space over itself.