Predicate logic sentence translation: "if only...then..."

Question

I'm a a bit stumped on symbolizing the sentence: "if only alcohol entices me, then I'm an alcoholic."

My initial thought was that by defining: $E(x)=$ x entices me, $a=$ alcohol, and $A=$ I'm an alcoholic.

Then wouldn't $\forall x(E(x)\land x=a\Rightarrow A$) or $\forall x((E(x)\Leftrightarrow x=a)\Rightarrow A$) work? But after a second thought, it seems like both symbolizations would still hold true even if $x\neq a$, since $(\mathbb{F}\Rightarrow\mathbb{T})\equiv\mathbb{T}$.

So something like the case of $x=$ juice would still make the symbolization true even though it shouldn't according to the original sentence.

Am I doing something wrong by attempting to apply "$\Rightarrow$" even though the original sentence is of the form "if...then..."?

Answer 1

You're very close!

The part 'only alcohol will entice me' translates to $\forall x (E(x) \rightarrow x=a)$, and since that is the antecedent of the conditional, the following will work:

$\forall x (E(x) \rightarrow x=a) \rightarrow A$