Background (subquestion): I am learning about the quantifiers $\forall$ and $\exists$. My book says that the proposition $$\forall x{\in} D\: P(x)$$ can be vacuously true, because it can be turned into the form $A\to B.$ For example, $$\forall x\,\big(3 { <} x {< }2\to x{>}0\big)$$ is a vacuous truth.

Then I naturally wonder whether $$\exists x{\in} D\:P(x)$$ can also become $A\to B.$ I believe that it's impossible, because the proposition seems to be molecular. (Being molecular means that it can't consist of smaller propositions, unlike, e.g., $E=P\to Q,$ which consists of propositions $P$ and $Q.$) But I don't know how to prove it.