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;

theorem
  x in dom f /\ X implies f.x = (f*(id X)).x
proof
  assume x in dom f /\ X;
  then x in X by XBOOLE_0:def 4;
  then (id X).x = x & x in dom id X by Th17;
  hence thesis by Th13;
end;
