In this paper we show that mismatched polar codes over symmetric B-DMCs symmetrized under the same permutation can achieve rates of at least I (W, V) bits whenever I (W, V) > 0, where W denotes the communication channel, V the mismatched channel used in the code design including both the encoder and decoder, and I(W, V) = Sigma(y) Sigma(x is an element of{0,1}) 1/2W(y vertical bar x) log(2) V(y vertical bar x)/1/2V(y vertical bar 0) + 1/2V(y vertical bar 1).