Definition:Classes of WFFs/Plain WFF

Definition
A plain WFF of predicate calculus is a WFF with no parameters.

Thus $WFF \left({\mathcal P, \varnothing}\right)$ is the set of all plain WFFs formed from $\mathcal P$.

Note that a WFF with parameters from $\mathcal K$ is, by definition, a WFF whose parameters are all in $\mathcal K$.

That is, none of its parameters come from outside of $\mathcal K$.

Hence a plain WFF is a WFF with parameters from $\mathcal K$ for all $\mathcal K$.