Exercise $7\mathrm{.}2\mathrm{.}3.$ Prove the following propositions. $($This exercise discusses two

forms of the "Existential Instantiation" rule. Please do not use the soundness

and completeness theorems.$)$

$(1)$ Syntactical form of the rule: Assume that the constant symbol $c$ does not

appear in the formulas $,$ and the set $$ of formulas, and

$c,$ then $\{EEx\}|--.$

$(2)$ Semantical form of the rule: Assume that the constant symbol $c$ does not

appear in the formulas $,$ and the set $$ of formulas, and

$c,$ then $\{EEx\}|==.$