Writing out Argument Question

For practice, I was writing out this argument for myself... I was wondering if it is "allowed" to make this leap: --- Premise) The desire to be praised is the desire to obtain favorable opinions of others. --> To be praised is to obtain the favorable opinions of others. -- I was thinking this could be done like factoring in algebra, i.e. the sufficient and necessary statements both have the phrase "the desire to" so I am wondering if I can "factor them out." --- I understand that this is not necessarily relevant to answering the question, I am just wondering for the sake of practicing writing out argument.