Where can I find a proof of the following general Steinitz exchange lemma:
Let $B$ be a basis of a vector space $V$, and $L\subset V$ be linearly independent. Then there is an injection $j:L\rightarrow B$ such that $L\cup(B\setminus j(L))$ is a disjoint union and a basis of the vector space $V$.
Or can someone suggest a proof of this result? Probably using Zorn's lemma.