In the formal mathematical definition, only modus ponens is allowed, since it's all that's needed and things should be kept simple. Anything else is considered to be a shorthand for several intermediate steps. --JG
There are many formalized logics, with corresponding formal notions of proof. For proof systems which can be nicely divided into axioms and inference rules, some of them have modus ponens as the only inference rule and others do not. (To some extent, it depends on whether you are using or studying the proof system. Formalized proof systems which are actually used, as in automatic theorem proving, tend to have more complex inference rules.) --Carl Witty
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