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 Th115:
  X c= Y implies R.:X c= R.:Y
proof
  assume
A1: X c= Y;
  let y be object;
  assume y in R.:X;
  then ex x st [x,y] in R & x in X by Def11;
  hence thesis by A1,Def11;
end;
