$$x:X.\; (P \land Q) \;\dashv\; \vdash \; \lnot \exists x: X.\; \lnot (\lnot P \lor \lnot Q)$$
I want to prove that the left hand side entails the right hand side using propositional and predicate logic. $P$ and $Q$ are of type $x$ and I can use natural deduction and axioms.
Thank you.