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We will start from the first given statement,
It doesn't matter if the variables are called x or called y, thus let us recall the variable in the second expression of the conjunction:
Using the commutative law,
Again using the commutative law,
Hence we can say that the statement ∀xP(x)∧∃xQ(x) is logically equivalent to ∀x∃y(P(x)∧Q(y)) where all quantifiers have the same nonempty domain.