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

theorem Th68:
  CnIPC (X) c= CnCPC (X)
proof
  let a be object;
  assume
A1: a in CnIPC (X);
  then reconsider r = a as Element of MC-wff;
  for T st T is CPC_theory & X c= T holds r in T
  proof
    let T such that
A2: T is CPC_theory and
A3: X c= T;
    T is IPC_theory by A2;
    hence thesis by A1,A3,Def15;
  end;
  hence thesis by Def20;
end;
