Given a valid deduction rule, based on a set of propositions, e.g.:
Prove that the statement:-
$(P_1 \land P_2 \land \ldots \land P_n) \to Q$.
is a tautology.
Now I know that when interpreting a deduction rule all premises in a deduction rule are conjoined together to imply the result. However this creates just a restatement of the latter statement which I'm trying to show is a tautology.
Is it really this simple? I.e. if I have two identical statements, and we know the first is true, then the second is true, so $T=T$.
Or do I have to prove the latter statement is a tautology using some knowledge from the deduction rule I haven't gathered?