I wonder if there is some short proof about the uniquness of the cardinality of a basis of a vector space (may be infinite). In proofwiki https://proofwiki.org/wiki/Bases_of_Vector_Space_have_Equal_Cardinality the contributor uses some elegant facts in set theory, including Hall's Marriage Theorem and Cantor-Bernstein theorem. Are there other ways?
Any references/solutions are welcomed. Thank you for your help.
