reserve X,Y for set;
reserve R for domRing-like commutative Ring;
reserve c for Element of R;

theorem Th9:
  for a being Element of R holds a <> 0.R implies a/a = 1.R
proof
  let A be Element of R;
  assume
A1: A <> 0.R;
  then (A/A) * A = A by Def4
    .= 1.R * A;
  hence thesis by A1,Th1;
end;
