reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;
reserve e,u for object,
  A for Subset of X;

theorem
  for X being set, f being X-valued Function for x being set st x in dom
  f holds f.x in X
proof
  let X be set, f be X-valued Function;
  let x be set;
  assume x in dom f;
  then
A1: f.x in rng f by Def3;
  rng f c= X by RELAT_1:def 19;
  hence thesis by A1;
end;
