This is a simple proof, and it makes sense logically, but I don't know how to show it. Any tips on how to prove stuff like this?

if V is a vector space with basis {v1,...,vn} and W is a subspace of V = sp(v3,..,vn)

show that if w E W and w = r1v1 + r2v2 for r1,r2 E R, then w = 0.

Well since V has a basis of v1...vn, that means that sp(v1...vn) = V.

All vectors in W can be written by a linear combination of v3...vn, thus if w is a linear combination of v1 and v2, and lies in W, that implies that it is the zero vector.