let p, q, s be Element of MC-wff ; :: thesis: (((p '&' q) '&' s) '&' q) => ((p '&' s) '&' q) in IPC-Taut
set P = (p '&' q) '&' s;
set Q = p '&' s;
A1: ((p '&' q) '&' s) => (p '&' s) in IPC-Taut by Lm8;
(((p '&' q) '&' s) => (p '&' s)) => ((((p '&' q) '&' s) '&' q) => ((p '&' s) '&' q)) in IPC-Taut by Th44;
hence (((p '&' q) '&' s) '&' q) => ((p '&' s) '&' q) in IPC-Taut by A1, Def14; :: thesis: verum