reserve X for OrtAfPl;
reserve o,a,a1,a2,a3,a4,b,b1,b2,b3,b4,c,c1,c2,c3,d,d1,d2,d3,d4,e1,e2 for
  Element of X;
reserve a29,a39,b29,x9 for Element of the AffinStruct of X;
reserve A,K,M,N for Subset of X;
reserve A9,K9 for Subset of the AffinStruct of X;

theorem Th2:
  for a,b ex c st LIN a,b,c & a<>c & b<>c
proof
  let a,b;
  consider p,q,r being Element of X such that
A1: LIN p,q,r and
A2: p<>q and
A3: q<>r and
A4: r<>p by Th1;
  reconsider a9=a,b9=b,p9=p,q9=q,r9=r as Element of the AffinStruct of X;
  LIN p9,q9,r9 by A1,ANALMETR:40;
  then consider c9 being Element of the AffinStruct of X such that
A5: LIN a9,b9,c9 and
A6: a9<>c9 and
A7: b9<>c9 by A2,A3,A4,TRANSLAC:1;
  reconsider c =c9 as Element of X;
  LIN a,b,c by A5,ANALMETR:40;
  hence thesis by A6,A7;
end;
