reserve x1, x2, x3, x4, x5, x6, x7 for set;

theorem Th23:
  for a being Rational, b being irrational Real st
  a <> 0 holds a / b is irrational
proof
  let a be Rational, b be irrational Real;
  assume
A1: a <> 0;
  assume a / b is rational;
  then reconsider c = a / b as Rational;
  c * b is irrational by A1,Th21,XCMPLX_1:50;
  hence thesis by XCMPLX_1:87;
end;
