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((id Y)*f) iff x in dom f & f.x in Y
proof
  dom((id Y)) = Y;
  hence thesis by Th11;
end;
