Prove that if the first symbol of $\alpha$ is a wff of a First order language, then there is a unique pos. integer i, and a unique wff $\beta$, such that $\alpha$ is $\forall v_i \beta$.
I am reasonably confident of my proof for $\alpha$ is of the form $\forall v_i \beta$ but I'm lost on how to actually prove that this i is unique and $\beta$ is unique. Maybe it could start with assume $\alpha = \forall v_i \beta_1 = \forall v_j \beta_2$ where $i \neq j$ and $\beta_1 \neq \beta_2$ but I don't know how to proceed from this.
Could someone give me some help on this one. I could only find answers to unique readability of sentential logic.