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
 X c= Y implies
 for R being X-valued Relation holds R is Y-valued
 proof assume
A1: X c= Y;
  let R be X-valued Relation;
   rng R c= X by Def17;
  hence rng R c= Y by A1;
 end;
