There are various synonyms for the phrase "to degree that," which is commonly used to indicate the extent to which something is true or applicable. One option is "to the extent that," which has a similar meaning. Another possibility is "in proportion to," which emphasizes the relationship between two variables, such as cause and effect. "Commensurate with" is another synonym that suggests a balanced or proportional relationship. Additionally, "correlated with" or "associated with" could be used to describe a connection between two things that increases or decreases in tandem. Overall, there are many different ways to convey the level or degree to which something is true or applicable, depending on the context and desired emphasis.