I have a question on if production rules of a formal grammar are being specified correctly. Wiki defines the syntax of grammars as the following finite set of production rules, where it states each rule of the form:

$(\Sigma \cup N)^{*}N(\Sigma \cup N)^{*} \implies (\Sigma \cup N)^{*}$

How can each rule have this form when each rule is a subset of the above arguments to the implication symbol? Should quantification and the $\in$ symbol be used to specify each rule? Thanks

I have a question on if production rules of a formal grammar are being specified correctly. Wikipedia defines the syntax of grammars as the following finite set of production rules, where it states each rule has the form:

$(\Sigma \cup N)^{*}N(\Sigma \cup N)^{*} \implies (\Sigma \cup N)^{*}$

How can each rule have this form when each rule is a subset of the above arguments to the implication symbol? Should quantification and the $\in$ symbol be used to specify each rule? Thanks