reserve G for IncProjStr;
reserve a,a1,a2,b,b1,b2,c,d,p,q,r for POINT of G;
reserve A,B,C,D,M,N,P,Q,R for LINE of G;

theorem Th10:
  G is configuration & {a1,a2} on A & a1<>a2 & b|'A implies a1,a2,
  b is_a_triangle
proof
  assume that
A1: G is configuration and
A2: {a1,a2} on A and
A3: a1<>a2 & b|'A and
A4: a1,a2,b are_collinear;
A5: a1 on A & a2 on A by A2,INCSP_1:1;
  ex P st a1 on P & a2 on P & b on P by A4,Th5;
  hence contradiction by A1,A3,A5;
end;
