theorem Th112:
  for A,B being set, f being Function of A,B st y in rng f ex x
  being Element of A st y = f.x
proof
  let A,B be set, f be Function of A,B;
  assume y in rng f;
  then consider x being object such that
A1: x in A and
A2: f.x = y by Th11;
  reconsider x as Element of A by A1;
  take x;
  thus thesis by A2;
end;
