reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem
  R|dom S = R|dom(S|dom R)
proof
  thus R|dom S = R|dom R|dom S
    .= R|(dom S /\ dom R) by Th65
    .= R|dom(S|dom R) by Th55;
end;
