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

theorem Th26:
  p => q in IPC-Taut & q => r in IPC-Taut implies p => r in IPC-Taut
proof
  assume that
A1: p => q in IPC-Taut and
A2: q => r in IPC-Taut;
  (p => q) => ((q => r) => (p => r)) in IPC-Taut by Th24;
  then (q => r) => (p => r) in IPC-Taut by A1,Def14;
  hence thesis by A2,Def14;
end;
