let p, q, s be Element of HP-WFF ; :: thesis: (p '&' (q '&' s)) => ((p '&' s) '&' q) in HP_TAUT
A1: ((q '&' s) '&' p) => ((p '&' s) '&' q) in HP_TAUT by Lm13;
(p '&' (q '&' s)) => ((q '&' s) '&' p) in HP_TAUT by Lm18;
hence (p '&' (q '&' s)) => ((p '&' s) '&' q) in HP_TAUT by A1, Th23; :: thesis: verum