theorem
  (for y st y in Y ex x st x in dom f & y = f.x) implies Y c= rng f
proof
  assume
A1: for y st y in Y ex x st x in dom f & y = f.x;
  let y be object;
  assume y in Y;
  then ex x st x in dom f & y = f.x by A1;
  hence thesis by Def3;
end;
