reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;

theorem Th3:
  for f being Function for x,y being object st f = [x,y] holds x = y
proof
  let f be Function, x,y be object;
  assume
A1: f = [x,y];
  then
A2: {x} in f by TARSKI:def 2;
A3: {x,y} in f by A1,TARSKI:def 2;
  consider a,b being object such that
A4: {x} = [a,b] by A2,RELAT_1:def 1;
A5: {a} = {a,b} by A4,ZFMISC_1:5;
A6: x = {a} by A4,ZFMISC_1:4;
  consider c,d being object such that
A7: {x,y} = [c,d] by A3,RELAT_1:def 1;
A8: x = {c} & y = {c,d} or x = {c,d} & y = {c} by A7,ZFMISC_1:6;
  then c = a by A5,A6,ZFMISC_1:4;
  hence thesis by A2,A3,A4,A5,A7,A8,FUNCT_1:def 1;
end;
