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

theorem Th17:
  for a,b being Element of R holds a <> 0.R & a * b = a implies b = 1.R
proof
  let A,B be Element of R;
  assume that
A1: A <> 0.R and
A2: A * B = A;
  set A1 = A/A;
  A1 = 1.R & (A * B)/A = (A/A) * B by A1,A2,Th9,Th11;
  hence thesis by A2;
end;
