# Is it true that every two Hamel Basis for a Vector Space have the same cardinality? [duplicate]

Let $X$ be a vector space over any field $F$, and let $\mathcal{B}$ and $\mathcal{C}$ Hamel basis for $X$. My question is

Is there a bijection $\phi : \mathcal{B}\to \mathcal{C}\ ?$ i.e. do $\mathcal{B}$ and $\mathcal{C}$ have the same cardinality?

We know this fact for finite dimensional vector spaces but, does this hold in general?

(Please ignore any concept of norm: I know that if $X$ is a Bannach space, then its dimension is at least $2^{\aleph_0}$, however, this doesn't prove my question, even in this case)