let p, q, s be Element of MC-wff ; :: thesis: ((p 'or' q) 'or' s) => (p 'or' (q 'or' s)) in IPC-Taut
(p 'or' q) => (q 'or' p) in IPC-Taut by Th56;
then A1: ((p 'or' q) 'or' s) => ((q 'or' p) 'or' s) in IPC-Taut by Th61;
(q 'or' p) => (p 'or' q) in IPC-Taut by Th56;
then A2: (s 'or' (q 'or' p)) => (s 'or' (p 'or' q)) in IPC-Taut by Th63;
((q 'or' p) 'or' s) => (s 'or' (q 'or' p)) in IPC-Taut by Th56;
then ((p 'or' q) 'or' s) => (s 'or' (q 'or' p)) in IPC-Taut by A1, Th26;
then A3: ((p 'or' q) 'or' s) => (s 'or' (p 'or' q)) in IPC-Taut by A2, Th26;
(s 'or' q) => (q 'or' s) in IPC-Taut by Th56;
then A4: (p 'or' (s 'or' q)) => (p 'or' (q 'or' s)) in IPC-Taut by Th63;
(s 'or' (p 'or' q)) => (p 'or' (s 'or' q)) in IPC-Taut by Th64;
then ((p 'or' q) 'or' s) => (p 'or' (s 'or' q)) in IPC-Taut by A3, Th26;
hence ((p 'or' q) 'or' s) => (p 'or' (q 'or' s)) in IPC-Taut by A4, Th26; :: thesis: verum