Propositional logic and tautologies Taken from P. Suppes "Introduction to logic" pp16

Starting from the sentence "If $P$ tautologically implies $Q$, then.."
Question: Is it true that, at least within propositional logic, we are able to prove only tautologies or do I mis-understand something?
If yes, is propositional logic special in some way? Is the notion of tautology meaningful only in propositional logic?
 A: *

*Suppose we are given the premiss '$P \land Q$', then we can of course trivially derive '$Q$'. Further, the premiss $P \land Q$' is said to tautologically entail the conclusion '$Q$' -- essentially because the corresponding conditional '$(P \land Q) \to Q$' is a tautology. 

*But note, '$P \land Q$' and '$Q$' themselves may not even true let alone be tautologies (perhaps '$P$' for example says 'Trump is a philosopher' and '$Q$' says 'Trump is a modest man'). That's fine. In propositional logic, we can prove a non-tautology, given one or more non-tautologies as premisses!

*However, if we are given no premisses to work with, if we have to rely on propositional logic reasoning alone, then yes, all we can prove in that case are tautologies.

*Is the notion of tautology meaningful only in propositional logic? Terminology varies. But I think mainstream usage is to reserve "tautology" primarily for sentences of the language of propositional logic that come out true on every line of the appropriate truth-table, and hence are provable from no premisses in an appropriate classical propositional logic. 

A: It's not difficult to see that the following assertions are equivalent.


*

*The statement $\mathcal B$ follows from the statements $\mathcal A_1, \mathcal A_2,\ldots ,\mathcal A_n$.

*The implication $\mathcal A_1\land\ldots\land\mathcal A_n\implies \mathcal B$ is a tautology.


Not as easy to suggest this might be the case, though, without any a priori intuition.
