reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;

theorem
  (for y st y in Y holds R"{y} <> {}) implies Y c= rng R
proof
  assume
A1: for y st y in Y holds R"{y} <> {};
  let y be object;
  assume y in Y;
  then R"{y} <> {} by A1;
  hence thesis by Th71;
end;
