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 Th75:
  T is CPC_theory iff CnCPC(T) = T
proof
  hereby
    assume
A1: T is CPC_theory;
A2: CnCPC(T) c= T
    by A1,Def20;
    T c= CnCPC(T) by Th72;
    hence CnCPC(T) = T by A2,XBOOLE_0:def 10;
  end;
  thus thesis;
end;
