reserve AS for AffinSpace;
reserve a,b,c,d,a9,b9,c9,d9,p,q,r,x,y for Element of AS;
reserve A,C,K,M,N,P,Q,X,Y,Z for Subset of AS;

theorem Th4:
  (a,b // A or b,a // A) & (a,b // c,d or c,d // a,b) & a<>b
  implies c,d // A & d,c // A
proof
  assume that
A1: ( a,b // A or b,a // A)&( a,b // c,d or c,d // a,b) and
A2: a<>b;
  a,b // A & a,b // c,d by A1,AFF_1:4,34;
  hence c,d // A by A2,AFF_1:32;
  hence thesis by AFF_1:34;
end;
