Validity of formulas with a certain prefix

In Mendelson 1987 (3rd ed.) there is an exercise on pp.74 that states:

"2.58 (a) Let A be any wf that contains no quantifiers, function
letters, or individual constants. Show that a closed prenex wf
(Ax1)...(Axn)(Ey1)...(Eym)A, with m>=0 and n>=1 is logically valid if
and only if it is true for every interpretation with a domain of n
objects."

Consider the sentence

1. (Ax1)(Ax2)(Ax3)(Ey1)(Ey2)(Ey3)[(x1=x1 & (x1=x2 -> (A(x1) <->
A(x2)))) -> (~y1=y2 & ~y1=y3 & ~y2=y3)]

in which (Ax3) occurs "vacuously" (which is well-formed according to
the formation rules stated on p.43). It formalizes the sentence "there
are at least 3 things (or equivalence classes)" and hence it is valid
in every interpretation with a domain of 3 objects. But it is not valid
since it fails in a domain of >3 objects.

So where have I gone wrong?

.

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