My logic exam is coming up and I'm pretty happy with my natural deductions, but I found this 'gem' in an old exam paper and for the life of me I cannot figure it out.
You need to prove $$ \forall x (P(x) \to Q(x)) \to (\forall x (P(x)) \to \forall x (Q(x)) $$ from no premises. The fact that there are no conjunctions or disjunctions makes this quite a tricky one, especially since there are 3 conditionals in there as well. I am trying to work backwards, ie. starting with the conclusion and working my way back up but even then I get stuck.
Any assistance would be greatly appreciated, thanks!