let p, q, s be Element of HP-WFF ; :: thesis: (p '&' (q '&' s)) => ((p '&' q) '&' s) in HP_TAUT
A1: (p '&' (s '&' q)) => ((p '&' q) '&' s) in HP_TAUT by Lm19;
(p '&' (q '&' s)) => (p '&' (s '&' q)) in HP_TAUT by Lm20;
hence (p '&' (q '&' s)) => ((p '&' q) '&' s) in HP_TAUT by A1, Th23; :: thesis: verum