How this statement should be written?

Question

If I have a theorem/conjecture of the form "Let $n$ be an [object with some properties], then $P(n)$", how would it be written in logic ? So I have 2 variants:
1)$\forall n \in A, P(n)$.
2)$(n\in A)\to(P(n))$.
(By $A$ I mean a set of all such objects with some property).
So is one of my variants right ? Or it should be written in some other form ?

Answer 1

$(n\in A)\to P(n)$ is a good start, but you need something to express the idea that you want this to be true for all $n$. So you should write $$ \forall n : \bigl[ n\in A \to P(n) \bigr] $$

This is what "$\forall n\in A. P(n)$" (with variations in punctuation that don't carry any meaning) is usually considered to be an abbreviation for in formal logic.