pedal circle passes through the anti steiner point?

Question

Given a triangle $\triangle ABC$ and $P$ is an arbitrary point. Let $\triangle DEF$ be the cevian triangle of $P$ with respect to (wrt) $\triangle ABC$ and $\triangle XYZ$ be the pedal triangle of $P$ wrt $\triangle ABC$. Is it true that the circumcircle of $\triangle XYZ$ intersects the circumcirle of $\triangle DEF$ at the Poncelet point of $A, B, C, P$ and the Anti Steiner point of $P$ wrt $\triangle DEF$? If so, how can we prove it?