# Are these production rules for a formal grammar?

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

The use of notation in that statement might be confusing. A grammar is a rule of the form "something $$\to$$ something", where the something on the left is a string of symbols containing at least one non-terminal symbol, and the something on the right is a string of symbols.
For instance, $$A \to BcD$$ would be a valid rule, as would $$AB \to BDeeF$$, or $$aAcE \to b$$.