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

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