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

theorem Th23:
  p => (q => r) in IPC-Taut implies q => (p => r) in IPC-Taut
proof
  assume
A1: p => (q => r) in IPC-Taut;
A2: ((p => q) => (p => r)) => ((q => (p => q)) => (q => (p => r))) in
  IPC-Taut by Th22;
  (p => (q => r)) => ((p => q) => (p => r)) in IPC-Taut by Def14;
  then ((p => q) => (p => r)) in IPC-Taut by A1,Def14;
  then
A3: ((q => (p => q)) => (q => (p => r))) in IPC-Taut by A2,Def14;
  q => (p => q) in IPC-Taut by Def14;
  hence thesis by A3,Def14;
end;
