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

theorem Th45:
  (( p => q ) '&' ( p '&' s )) => ( q '&' s ) in IPC-Taut
proof
  set P = p => q, Q = p '&' s, S = q '&' s;
A1: P => (Q => S) in IPC-Taut by Th44;
  ( P => ( Q => S )) => (( P '&' Q ) => S ) in IPC-Taut by Th37;
  hence thesis by A1,Def14;
end;
