Accepted fact is a statement that is generally agreed upon by a majority of people. However, there are many synonyms that can be used instead of this phrase. Some of the alternatives include "established truth," "common knowledge," "settled belief," "undeniable reality," "irrefutable evidence," "conclusive proof," "proved certainty," and "axiomatic principle." These synonyms can help writers and speakers to avoid repetition and add variety to their language. It is important to choose the synonym that best fits the context and meaning of the statement being made.