This is a good example of how much better we are at informal logic than formal logic. If I said that I have to mail a letter and I also have cut the grass and mail a letter, you would probably suspect there is something wrong with me, since it is obvious that I could have just said that I have to cut the grass and mail a letter. You could use this intuition to provide another way of showing the statement is equivalent to Y AND X.
The statement is true if and only if Y is true and both X and Y are true. But if both X and Y are true then it must be the case that Y is true, so the first part is redundant and we are left with just Y AND X.
.