Axiom of union - singleton case

Question

I have a question concerning the axiom of union. We know that the axiom states that given a set $A$, there is a set $U$ which contains all elements of the elements of $A$. It is clear that if $A=\lbrace \lbrace 1, 2\rbrace, \lbrace 2, 5, 6\rbrace \rbrace$, then $U=\lbrace 1, 2, 5, 6\rbrace$. Now, what happens if $A=\lbrace 7\rbrace$? We would have $U=\lbrace x | \ \exists a\in A, x\in a\rbrace=\lbrace x | x\in 7\rbrace=...?$. I know that 7 is also considered as being a set in the axiomatic theory, but I don't understand how do we conclude who $U$ actually is in this case.