This technique pretty much describes the rule of replacement in formal propositional logic called EXPORTATION.

i.e., [p --> (q --> r)] is logically equivalent to [(p AND q) --> r]

In other words, the "domain" is p. The given statement is, "if p, then q if r." In the "domain" of p, the statement can be simplified to "q if r." In other words, [p --> (q --> r)]. Re-stating this conditional statement WITHOUT "kicking it up to the domain" would yield: "if p AND q, then r," or, in other words, "[(p AND q) --> r]."