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

theorem Th29: :: Contraposition
  (p => (q => r)) => (q => (p => r)) in IPC-Taut
proof
A1: q => (p => q) in IPC-Taut by Def14;
  (p => (q => r)) => ((p => q) => (p => r)) in IPC-Taut by Def14;
  then
A2: (p => q) => ((p => (q => r)) => (p => r)) in IPC-Taut by Th23;
  ((p => q) => ((p => (q => r)) => (p => r))) => ((q => (p => q)) => (q =>
  ((p => (q => r)) => (p => r)))) in IPC-Taut by Th22;
  then (q => (p => q)) => (q => ((p => (q => r)) => (p => r))) in IPC-Taut by
A2,Def14;
  then (q => ((p => (q => r)) => (p => r))) in IPC-Taut by A1,Def14;
  hence thesis by Th23;
end;
