Where does “fantasear” come from?

fantasear (Spanish) comes from Spanish fantasía, from Latin phantasia, from Ancient Greek φαντασία, from Ancient Greek φᾰ́ντᾰσῐς, from Ancient Greek φᾰντᾰ́ζω, from Ancient Greek φαίνω, from English -type, from Ancient Greek τύπος — to push, to hit.

Ancestry of “fantasear”, step by step

Step	Language	Word	Meaning
1	Spanish	fantasía	fantasy; costume jewellery; make-believe
2	Latin	phantasia	fancy, idea, notion; fantasy; phantom,...
3	Ancient Greek	φαντασία	look, appearance, presentation, display; showy...
4	Ancient Greek	φᾰ́ντᾰσῐς	—
5	Ancient Greek	φᾰντᾰ́ζω	make visible; to make visible, show; to become...
6	Ancient Greek	φαίνω	I cause to appear, bring to light; I show,...
7	English	-type	impressed form; stamp; print; typical form; Used...
8	Ancient Greek	τύπος	A blow, pressing; The results of a blow: mark,...
9	Ancient Greek	τύπτω	to beat, strike, smite; to beat, strike oneself
10	Proto-Indo-European	(s)tewp-	to push, to stick
11	Proto-Indo-European	(s)tew-	to push, to hit

Every word from Proto-Indo-European (s)tew- →