
theorem Th53:
  for R,S being non degenerated almost_left_invertible commutative
  Ring for f being Function of R, S st f is RingHomomorphism for x,y being
  Element of R st y <> 0.R holds f.(x * y") = f.x * (f.y)"
proof
  let R,S be non degenerated almost_left_invertible commutative Ring;
  let f be Function of R, S;
  assume
A1: f is RingHomomorphism;
  let x,y be Element of R;
  assume
A2: y <> 0.R;
  thus f.(x * y") = f.x * f.(y") by A1,GROUP_6:def 6
    .= f.x * (f.y)" by A1,A2,Th52;
end;
