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 Th24:
  P c= Q implies P*R c= Q*R
proof
  assume
A1: P c= Q;
  let x,y;
  assume [x,y] in P*R;
  then ex z st [x,z] in P & [z,y] in R by Def6;
  hence thesis by A1,Def6;
end;
