How do I prove that if $A \neq B$, then $\{A\} \neq \{B\}$, where $A$, $B$ are sets?

Question

This is in ZFC, and I thought it looked trivial, so I didn't give it much thought at first, but I've tried it now for some time with no progress.

I'd like to keep the proof as short as possible. Would really appreciate some hints :)

Answer 1

by contradiction: $$\text{ if } \{A\}=\{B\} \text{ then }A=\bigcup \{A\}=\bigcup\{B\}=B$$

Answer 2

Notice that $A\in \{A\}$ and $A\not\in \{B\}$