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 Th65:
  (R|X)|Y = R|(X /\ Y)
proof
  let x,y;
A1: [x,y] in R|X iff [x,y] in R & x in X by Def9;
A2: [x,y] in R|(X /\ Y) iff [x,y] in R & x in X /\ Y by Def9;
  [x,y] in (R|X)|Y iff [x,y] in R|X & x in Y by Def9;
  hence thesis by A1,A2,XBOOLE_0:def 4;
end;
