I have just started studying predicate logic and I don't perfectly know how to use the quantifiers yet in formulas, so I have this short question:
Does the following hold? $$\forall x(A \to B) \iff (\forall xA \to \forall xB)$$ So if I have the quantifier outside of the parentheses, can I apply it to every formula inside the parentheses?
I'm sorry if I have used some wrong terminology, I'm not used to talking about mathematics in english.
Thanks!