Is it possible Sony's continued support of the PSP hurts the Vita?

[KHlover]

HokageTenshi said:

don't forget Vita is able to play PSP games, so i dont see why Sony stopping PSP market since there are still many developers not investing on Vita yet...
most important is is selling each PSP let Sony earn more profit than selling each Vita...
PSP are just for users who still can't afford to pay for Vita but still had a choice to play certain good games for the time being, never worry Vita will slowly totally take over PSP market when production cost gets cheaper, just give Vita some times... ^^

Vita is not able to play PSP games. You can't use PSP games you already bought with the Vita (no UMD support and no way to create ISO's and transfer them), instead you have to buy them all over again. The Wii can play GCN games, the DS can play GBA games and the 3DS can play DS games. Vita CAN'T play PSP games. 

@topic

Seeing how the PSP still manages 2/3 of Vita sales it certainly seems so. Killing of PSP is no option though, as it still makes some money.