reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem Th20:
  for f being PartFunc of X,{y} st x in dom f holds f.x = y
proof
  let f be PartFunc of X,{y};
  x in dom f implies f.x in {y} by Th4;
  hence thesis by TARSKI:def 1;
end;
