theorem Th66:
  (X |-_IPC p & X c= Y) implies Y |-_IPC p
proof
assume
A1: X |-_IPC p & X c= Y; then
  p in CnIPC(X); then
  ex f st f is_a_proof_wrt_IPC X & Effect_IPC(f) = p by Th16; then
  consider g such that L: g is_a_proof_wrt_IPC X & Effect_IPC(g) = p;
    g is_a_proof_wrt_IPC Y & Effect_IPC(g) = p by L,A1,Th10; then
  p in CnIPC(Y) by Th16;
  hence thesis;
end;
