Exist

google

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early 17th century: probably a back-formation from existence.

wiktionary

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From French exister, from Latin existō(“to stand forth, come forth, arise, be”), from ex(“out”) + sistere(“to set, place”), caus. of stare(“to stand”); see stand. Compare assist, consist, desist, insist, persist, resist.

etymonline

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exist (v.)

"to have actual being of any kind, actually be at a certain moment or throughout a certain period of time," c. 1600, from French exister (17c.), from Latin existere/exsistere "to step out, stand forth, emerge, appear; exist, be" (see existence). "The late appearance of the word is remarkable" [OED]. Middle English often used ibēn, ibeon (based on be) for "to exist." Related: Existed; existing.