As I read in this thread, the difference between propositional and predicate logic is that in predicate logic you can use things like quantifiers, predicates and functions whereas in propositional logic you cannot.
However, you can use things like letters, $\wedge$, $\vee$, $\neg$ in both propositional and predicate logic.
Does this mean that everything we can use in propositional logic we can use in predicate logic? In other words, propositional logic $\subset$ predicate logic?