Let's consider any formula expressed in the first order logic. Let $p,q$ be variables, $S$ is a structure. $S = <S_s, \Sigma_f, \Sigma_r> $
Let $\phi = p \implies q $ Now, to the formula be a true $p$ must be not satisfied or $q$ must be satisfied.
But how to think about satisfable in the sense of variables?
If $p,$q were relations it would be obvious because it depends on $\Sigma_r$.
In first order logic, the variables take only values from the domain of discourse, which is usually not the boolean domain.
And prime formulas have the form $r(t_1,..,t_n)$, where $r$ is a relation symbol and $t_1,..,t_n$ are terms.
You can do what you want in higher order logics, but not in first order logic, i.e. quantify over propositional variables or relation symbols.
In higher order logic you can then use these variables in places of a relation symbol.