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 Th134:
  P c= R implies P"Y c= R"Y
proof
  assume
A1: P c= R;
  let x be object;
  assume x in P"Y;
  then ex y st [x,y] in P & y in Y by Def12;
  hence thesis by A1,Def12;
end;
