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 f being X-valued Function st x in dom f holds f.x is Element of X
 proof let f be X-valued Function;
  assume x in dom f;
   then
A1: f.x in rng f by Def3;
   rng f c= X by RELAT_1:def 19;
  hence f.x is Element of X by A1;
 end;
