let p, q, s be Element of HP-WFF ; :: thesis: ((p '&' q) '&' s) => (p '&' (s '&' q)) in HP_TAUT
A1: ((s '&' q) '&' p) => (p '&' (s '&' q)) in HP_TAUT by Th43;
((p '&' q) '&' s) => ((s '&' q) '&' p) in HP_TAUT by Lm13;
hence ((p '&' q) '&' s) => (p '&' (s '&' q)) in HP_TAUT by A1, Th23; :: thesis: verum