Seeking a proof equivalent to the story "She said that I would stop her if she told me why she is leaving, so I decided to stop her anyway!" I am looking for an interesting mathematical proof which is equivalent to the story:

"She said that I would stop her if she told me why she is leaving, so I decided to stop her anyway!"

Mathematically, I guess, this could be phrased, for a language $\mathcal L$ in propositional logic, as:
$$\Big(\exists A\in Prop(\mathcal L) \,\,\text{s.t.}\,\,\vdash A\,\,\&\,\, A\implies B\Big)\implies B. $$
I am no logician and probably am wrong regarding to the last part, so please correct me, as long as my informal description is clear.
Edit: Clearly, there are many situations where you know
\begin{align*}
\vdash& A\\
\vdash& A\implies B\vee C\\
\vdash& (B\implies D)\&(C\implies D)\\
&\quad\Downarrow\\
\vdash& D\end{align*} 
For example, have a function with two fixed points, each of which is rational, and have a convergent recursive sequence defined by this function. You know it converges to a fixed point but you do not know to which, however you do know that the limit is rational.
$\textbf{Edit:}$
In my example, it looks like $A$ could be "She was leaving to save her brother from Dracula" and $B$ is "I stopped her from leaving".
 A: The original phrase

She said that I would stop her if she told me why she is leaving, so I decided to stop her anyway!"  $~(0)$

The phrase $(0)$ reads as $(1)$, which is logically equivalent to the statement $B$. In $(1)$, I have symbolized "I stopped her" as $B$, and "she told me why she is leaving" as $W$.
\begin{equation}\tag{1}
(W\rightarrow B)~\&~B
\end{equation}
Careful reading of $(0)$ shows that the girl did not explain why she was leaving, so it's not necessary for the other person to stop her.
Your statement
\begin{equation}\tag{2}
\Big(\exists A\in Prop(\mathcal L) \,\,\text{s.t.}\,\,\vdash A\,\,\&\,\, A\implies B\Big)\implies B
\end{equation}
There are a few nuances with (2). To best state explicitly that the right hand side of $(2)$ is a sentence in propositional logic, you should bind both $A$ and $B$, as opposed to just $A$.
Secondly, you have placed the quantification and meta level proof symbol ($\vdash$), in the antecedent of your implication using brackets. This means that $(2)$ is equivilent to $(3)$, which is clearly not what you intended to say.
\begin{equation}\tag{3}
\big(\exists A\in Prop(\mathcal L) \,\,\text{s.t.}\,\,\nvdash A\,\,\&\,\, A\implies B\Big)\lor B
\end{equation}
A better symbolization of $(3)$ is $(4)$.
\begin{equation}\tag{4}
\exists A,B \in Prop(\mathcal L) \,\,\text{s.t.}\,\,\vdash (A\,\,\&\,\, A\implies B)\implies B
\end{equation}
Your first edit
Your edit is a lot clearer, and the symbolization for this statement is good. It has a different logical form to $(0)$ however, and appears to be unrelated.
