Whenever we use the string
We are using a meta variable, in this case $x$, which stands for any object in the reference set.
However, the semantics of the symbol $forall$ indicate that we are refering to all objects that satisfy certain condition $P(x)$.
So, the semantics of “for all the objects over which the metavariable varies, $P(x)$” but we know, a priori, that the meta variable already refers to all the objects in the reference set.
This looks redundant to me.
So, is the universal quantifier redundant?