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
A1: (s 'or' (p 'or' q)) => ((p 'or' q) 'or' s) in IPC-Taut by Th56;
  (q 'or' s) => (s 'or' q) in IPC-Taut by Th56;
  then
A2: (p 'or' (q 'or' s)) => (p 'or' (s 'or' q)) in IPC-Taut by Th63;
  (p 'or' (s 'or' q)) => (s 'or' (p 'or' q)) in IPC-Taut by Th64;
  then (p 'or' (q 'or' s)) => (s 'or' (p 'or' q)) in IPC-Taut by A2,Th26;
  hence thesis by A1,Th26;
end;
