>>3\(¬ \exists x/ standfor(man,x) \iff \forall x, ¬standfor(man,x) \)"There does not exist an x such that the man stands for x, if and only if for all x the man does not stand for x."
This is the application of a valid logical rule. From wikipedia:
"Generally, then, the negation of a propositional function's existential quantification is a universal quantification of that propositional function's negation; symbolically,
\({\displaystyle \lnot \ \exists {x}{\in }\mathbf {X} \,P(x)\equiv \ \forall {x}{\in }\mathbf {X} \,\lnot P(x)}\)(This is a generalization of De Morgan's laws to predicate logic.)"
https://en.wikipedia.org/wiki/Existential_quantification#NegationThank you for your wisdom, Anon.