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fui, fue, fui-, fuer-, fues- Preterite, imperfect, and future conjugation stems in verbs ser and ir.
From their respective forms in Latin fui, fue, fui-, fuer-, fues- with the meaning of "become."

From Proto-Italic stem *fu- "to become." From Proto-Indo-European *bhh2u̯- 'id.'

Note that present and future indicative derive from Latin sedere "to sit." The verb collapsed sedere and essere "to be" with fui into a single new verb meaning "to be."

The forms appearing in ir were drawn from the verb ser.