Name of this theorem? In $\angle BAC$, if $AM$ and $AN$ are isogonal, and $P=MB\cap CN$ and $T=BN\cap CM$, then $AP$ and $AT$ are isogonal

Question

Recently I was told of the theorem in Euclidean geometry that says the following:

Suppose we have $\angle BAC$ and two isogonal* lines $AM$ and $AN$. If $BM\cap CN=P$ and $BN\cap CM=T$, then $AP$ and $AT$ are isogonal lines.

Is there some common name for this theorem ?

*By isogonal lines I mean lines that are symmetric with respect to angle bisector.