The word "subproposition" refers to a statement or proposition that supports a larger argument or theory. If you are looking for alternate synonyms, you could use the term "substatement" or "subsidiary proposition." Other possibilities might include "supporting evidence," "interdependent argument," or "subordinate claim." Depending on the context, you could also consider using words like "collateral evidence," "corroborating argument," or "auxiliary statement." Regardless of which term you choose, the goal is to communicate a related idea that bolsters or strengthens the main point you are trying to make. By using synonyms effectively, you can add depth and complexity to your writing, while also improving your clarity and precision.