reserve S for IncStruct;
reserve A,B,C,D for POINT of S;
reserve L for LINE of S;
reserve P for PLANE of S;
reserve F,G for Subset of the Points of S;
reserve a,b,c for Element of {0,1,2,3};
reserve S for IncSpace;
reserve A,B,C,D,E for POINT of S;
reserve K,L,L1,L2 for LINE of S;
reserve P,P1,P2,Q for PLANE of S;
reserve F for Subset of the Points of S;

theorem Th35:
  A <> B & C on Line(A,B) implies {A,B,C} is linear
proof
  assume A <> B;
  then {A,B} on Line(A,B) by Def19;
  then
A1: A on Line(A,B) & B on Line(A,B) by Th1;
  assume C on Line(A,B);
  then {A,B,C} on Line(A,B) by A1,Th2;
  hence thesis;
end;
