When you say "x is not equal to 7, 11, or 15", what you are really saying is that "x is not equal 7, and x is not equal to 11, and x is not equal to 15". Therefore, the expression should be:
($ID != 7 && $ID != 11 && $ID != 15)
equivalently, you are saying "it is not the case that x is equal to 7, or x is equal to 11, or x is equal to 15":
(!($ID == 7 || $ID == 11 || $ID == 15))