reserve T, X, Y for Subset of HP-WFF;
reserve p, q, r, s for Element of HP-WFF;

theorem Th43:
  ( p '&' q ) => ( q '&' p ) in HP_TAUT
proof
  set P = p '&' q;
A1: P => q in HP_TAUT by Def10;
A2: P => p in HP_TAUT by Def10;
  ( P => q ) => (( P => p ) => ( P => ( q '&' p ))) in HP_TAUT by Th35;
  then ( P => p ) => ( P => ( q '&' p )) in HP_TAUT by A1,Def10;
  hence thesis by A2,Def10;
end;
