There are many synonyms available for the phrase "saw one's uncle". Some alternative ways to express this could include "encountered one's uncle", "ran into one's uncle", or "met up with one's uncle". You could also describe the meeting more specifically, using phrases like "had a chance encounter with one's uncle" or "bumped into one's uncle unexpectedly". Alternatively, you could use more formal language to convey the same sentiment, such as "had the pleasure of meeting one's uncle" or "crossed paths with one's uncle". Whatever the phrasing used, the idea is that the speaker had an unplanned meeting with their uncle.
