Establish this logical equivalence, where x does not occur as a free variable in A. Assume that the domain is nonempty.
∀x(A → P(x)) ≡ A → ∀xP(x)
How in the heck am I supposed to do this? Am I supposed to prove (translating the logical statement into English in bold) for every value of A there is a value that makes A true is equivalent to there is some value for A that makes A true?