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

theorem
  ( p '&' (s '&' q) ) => ( p '&' (q '&' s) ) in HP_TAUT
proof
  set P = s '&' q, Q = q '&' s;
A1: P => Q in HP_TAUT by Th43;
  ( P => Q ) => (( p '&' P ) => ( p '&' Q )) in HP_TAUT by Th46;
  hence thesis by A1,Def10;
end;
