Let us first look at the examples.
Example 1 a1 : (All x) ((Exist y) (f(x,y))) by
Therefore, ARRN is used to take out the unnecessary parentheses in between the quantitization blocks. Also, it can be used to insert parentheses.
Example 2 a1 : (All x) (All y) (g(x,y)) by ...;
Thus, ARRN is an abbreviation of arrange.