Can the rules of inference of propositional logic be applied to open formulae in first-order logic?

Question

Where $a$ and $b$ are free variables:

1. $\forall xPx$ Premise
2. $Pa$ Universal Instantiation 1
3. $Pb$ Universal Instantiation 1
4. $Pa\land Pb$ Adjunction 2,3
5. $\forall x(Px\land Pb)$ Universal Generalization 4
6. $\forall x,y(Px\land Py)$ Universal Generalization 5

Is the step-4 rule of inference, adjunction from propositional logic, valid? $Pa$ and $Pb$ are open formulae and thus not sentences and do not represent propositions.