let S be IncSpace; :: thesis: for A, B, C being POINT of S st not {A,B,C} is linear holds
Plane (A,B,C) = Plane (A,C,B)
let A, B, C be POINT of S; :: thesis: ( not {A,B,C} is linear implies Plane (A,B,C) = Plane (A,C,B) )
assume A1: not {A,B,C} is linear ; :: thesis: Plane (A,B,C) = Plane (A,C,B)
then not {A,C,B} is linear by ENUMSET1:57;
then {A,C,B} on Plane (A,C,B) by Def20;
then {A,B,C} on Plane (A,C,B) by ENUMSET1:57;
hence Plane (A,B,C) = Plane (A,C,B) by A1, Def20; :: thesis: verum