Implicit function theorem, a particular case.

Question

I have a question regarding the correct use of the implicit function theorem. Suppose I have the following equation:

\begin{equation} P = f (\xi,Y) \end{equation}

I'm interested in the effect of $\xi$ on the $Y$ variable. For this, I would like to define:

\begin{equation} F(\xi,Y) = P - f (\xi,Y) = 0 \end{equation}

I think I can't use the implicit function theorem according to the following formula:

\begin{equation} \frac{\partial Y}{\partial \xi } = - \frac{ \frac{\partial F}{\partial \xi } }{ \frac{\partial F}{\partial Y } } \end{equation}

Because $\frac{\partial F}{\partial Y } = \frac{\partial P}{\partial Y } - \frac{\partial f}{\partial Y } = 0 $, since $P = f(\xi , Y)$.

Is this right? Or should I treat the variable $P$ as a constant?