Where does “antémétique” come from?

antémétique (French) comes from French émétique, from Latin emeticus, from Ancient Greek ἐμετικός, from Ancient Greek ἔμετος, from Ancient Greek ἐμέω, from Ancient Greek ϝεμέω, from Proto-Indo-European *wémh₁ti, from Proto-Indo-European wemh₁- — to spew, to vomit.

Ancestry of “antémétique”, step by step

Step	Language	Word	Meaning
1	French	émétique	emetic; an emetic
2	Latin	emeticus	emetic, turning the stomach
3	Ancient Greek	ἐμετικός	provoking sickness
4	Ancient Greek	ἔμετος	vomiting, sickness; vomit
5	Ancient Greek	ἐμέω	I vomit, throw up, am sick
6	Ancient Greek	ϝεμέω	—
7	Proto-Indo-European	*wémh₁ti	to vomit
8	Proto-Indo-European	wemh₁-	to spew, to vomit

Every word from Proto-Indo-European wemh₁- →Every word from Proto-Indo-European *wémh₁ti →Every word from Ancient Greek ϝεμέω →