theorem Th5:
  for a,b holds a,a // b,b
proof
  let a,b;
  now
    consider c such that
A1: a,c // c,b by Def1;
    assume
A2: a<>b;
    c,a // c,b by A1,Th4;
    hence thesis by A2,Def1;
  end;
  hence thesis by Def1;
end;
