Which logical rules are used in combining universal quantifiers with same conditional

quantifiers logic first-order-logic predicate-logic

What Wiki calls the Composition Rule seems to be the one that combines implications:

$$ ((p \rightarrow q)\land (p\to r)) \Leftrightarrow (p \rightarrow (q\land r)) $$

So would the correct order here be Universal Instantiation (aka Universal Elimination), Composition, then Universal Generalization (aka Universal Introduction)? Not sure

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