"Deeply entrenched" is a term that typically describes something that is firmly established and difficult to change. Synonyms for this phrase include "firmly established," "ingrained," "rooted," "entrenched," "well-established," "fixed," "set," "established," "hardened," and "immutable." These terms all convey the idea of something that is deeply embedded in a particular system or culture, and which is nearly impossible to uproot or overturn. Whether used to describe traditional values, political institutions, or cultural norms, these synonyms suggest a certain degree of permanence and resistance to change that can be challenging to overcome. Nevertheless, it is important to recognize the existence and influence of these entrenched forces in our lives, as we strive to make progress toward a more just and equitable society.