Combine the softened cream cheese, Greek yogurt, sugar and vanilla in a large bowl, and whip together until very smooth. Then add the eggs, one at a time, mixing until just combined.
Pour the filling into the springform pan, being careful to fully cover the crust around the edges (if any crumbs are exposed, they can become soggy from the moisture in the pressure cooker).
Place a trivet rack into the pressure cooker, and pour in 1 cup of water. Place the cheesecake on top of the trivet and close the lid. Set the valve to sealing position, and cook on high pressure for 30 minutes (on the Instant Pot, select "Manual" and use the default setting).
After the cooking time is up and the pressure has released naturally, open the lid and use the trivet handles to lift out the pan. If water has settled on top of the cheesecake, gently blot any excess with a paper towel. Allow the cheesecake to cool on a rack at room temperature for 1-2 hours, then transfer it to the refrigerator to chill completely (at least 4 hours).