let p, q, s be Element of HP-WFF ; :: thesis: ((s '&' q) '&' p) => ((q '&' s) '&' p) in HP_TAUT
set P = s '&' q;
set Q = q '&' s;
A1: (s '&' q) => (q '&' s) in HP_TAUT by Th43;
((s '&' q) => (q '&' s)) => (((s '&' q) '&' p) => ((q '&' s) '&' p)) in HP_TAUT by Th41;
hence ((s '&' q) '&' p) => ((q '&' s) '&' p) in HP_TAUT by A1, Def10; :: thesis: verum