A universal generalisation is $$ \boxed{\begin{array}{c} \underline{P(c) \textsf{ for any arbitrary entity } c \textsf{ in the domain}} \\ \forall x P(x)\end{array}} $$
By universal generalisation, given the premise takes place for a generic object of the domain, we may derive :
The object in the premise of must not be specific but arbitrary, i.e. we cannot make any assumption about other than it comes from the domain. Universal generalisation can be seen as .