Every philosophical empiricist admires Humes. Some philosophical idealists like no one who admires Humes. Therefore, some philosophical idealists like no philosophical empiricists.
$\forall x(Ex \implies Hx)$
$\exists x(Ix \land \forall y(Hy \implies -Lxy))$
$\therefore$ $\exists x(Ix \land \forall y(Ey \implies -Lxy))$
is this correct?
My lack of confidence stems around the conclusion, intuitively (in my mind) it reads: There is a philosophical idealist say x with that property that if y is an arbitrary philosophical empiricists then x does not like y.
However it could also read: $\exists x(Ix \land -\forall y(Ey \implies Lxy))$
I.e. There is a philosophical idealist that does not like any philosophical empiricist
Your answer is correct. Unlike in our previous exercise, there is no negation ambiguity here because the word "no" is firmly referring to the count of Empiricists.