reserve i,j,k,n for Nat;

theorem Th3:
  for f being Function, x,y being object st f"{y} = {x} holds x in dom
  f & y in rng f & f.x = y
proof
  let f be Function, x,y be object;
  assume f"{y} = {x};
  then
A1: x in f"{y} by TARSKI:def 1;
  hence
A2: x in dom f by FUNCT_1:def 7;
  f.x in {y} by A1,FUNCT_1:def 7;
  then f.x = y by TARSKI:def 1;
  hence thesis by A2,FUNCT_1:def 3;
end;
