This paper investigates the relations between implication functions, modus ponens and conjunctions. For that purpose, a review of fuzzy modus ponens is done, that takes into account the different worlds involved in the inference. This leads to consider two new modalities of that rule, the Modus Intusconiugando Ponens and the Modus Forisconjugando Ponens from which Internal and External conjunctive conditional relations respectively follows. In addition, given such formulation, the modus ponens inequalities can be studied.