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
  dom R \ dom(R|A) = dom(R \ (R|A))
proof
  thus dom R \ dom(R|A) = dom R \ A /\ dom R by Th55
     .= dom R \ A by XBOOLE_1:47
     .= dom(R \ (R|A)) by Th167;
end;
