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

theorem
  (p '&' q) in HP_TAUT implies (q '&' p) in HP_TAUT
proof
    assume
A1: p '&' q in HP_TAUT;
    then
A2: q in HP_TAUT by Th31;
    p in HP_TAUT by A1,Th31;
    hence thesis by A2,Th31;
end;
