
theorem Th1:
  for A,B being non empty set, f being Function of A,B holds
    f is one-to-one iff
    for a,b being Element of A st f.a = f.b holds a = b
proof
  let A,B be non empty set;
  let f be Function of A,B;
  thus f is one-to-one implies
  for a,b being Element of A st f.a = f.b holds a = b by FUNCT_2:19;
  assume for a,b being Element of A st f.a = f.b holds a = b;
  then for a,b being object st a in A & b in A & f.a = f.b holds a = b;
  hence thesis by FUNCT_2:19;
end;
