Discrete Math - Predicate and Propositional logic

C. While the quantifiers V and 3 are by far the most common, there are some other quantifiers that are sometimes used. For example, some people use ]! c ( Z : P(x) to denote "there exists a unique r ( Z such that P(x)" which is true when there is one and only one value of r in the set Z such that P(x) is true. Prove that 3! is "syntactic sugar," in that for any expression y that uses are Z : P(x), there is a logically equivalent y that uses only the quantifiers V and 3; standard propositional logic notation (A, -, V, =); standard equality/inequality notation (=, 2, ); and the predicate P in the question. Don't forget to follow the general syntax of predicate logic. You cannot use shorthand such as Vy