Given $\mathcal{F}$ is a field and $\alpha \in \mathcal{F}$. Prove that $$0+\alpha=\alpha$$
Since existence of additive identity $0$ is part of axioms, I don't understand how to prove this statement.
EDIT: Exact Statement from Page2 of Finite-Dimensional Vector Spaces:
Almost all the laws of elementary mathematics are consequences of the axioms defining a field. Prove, in particular, that if $\mathcal{F}$ is a field and if $\alpha$ belongs to $\mathcal{F}$, then following relationship hold
$$(a) \hspace{5mm} 0+\alpha=\alpha$$