written proof – Prove that if $ {7k: k in {Z} } subsetneq {nm: m in {Z} } $, then n = 1.

Let n be a natural number. Prove that if $ {7k: k in {Z} } subsetneq {nm: m in {Z} } $, then n = 1.

I know that we have to show $ x in {A} $ involved $ x in {B} $, and that there is $ x in {B} $ such as $ x notin {A} $. Which means that $ x in {A} neq {x in {B}} $.
Any help is welcome, thank you!