Hah, I don't blame you. I had to do a double (or triple) take.I misread it, thought that the corollary was about dependance too.
I'm saying - if the corollary was talking about dependence, a consequence would be that any subset of a vector space is linearly dependent because the vector space itself is.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.