reserve T, X, Y for Subset of MC-wff;
reserve p, q, r, s for Element of MC-wff;

theorem
  ( (p 'or' q) 'or' s ) => ( p 'or' (q 'or' s) ) in IPC-Taut
proof
  (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 thesis by A4,Th26;
end;
