$3.$ Existential Generalization $($EG$)$

Existential generalization$$is a rule of inference in natural deduction for predicate logic. Existential generalization allows you to obtain a particular statement $[$a statement governed by an existential quantifier such as $($x$),($y$),($z$),$ etc.$]$ from an expression containing one or more constants or free variables. Existential generalization is defined as follows: