The Lindemann-Weierstrass Theorem states the following:
If $\alpha_1,\dots,\alpha_n$ are $\mathbb Q$-algebraic and $\mathbb Q$-linearly independent, then $\mathrm e^{\alpha_1},\dots,\mathrm e^{\alpha_n}$ are $\mathbb Q$-algebraically independent.
Baker's reformulation is the following:
If $\alpha_1,\dots,\alpha_n$ are distinct $\mathbb Q$-algebraic, then $\mathrm e^{\alpha_1},\dots,\mathrm e^{\alpha_n}$ are $\overline{\mathbb Q}$-linearly independent.
It is clear why Baker's reformulation implies the actual theorem, but how can the converse be proven?