Is it safe to seed PRNG with sequences from CSPRNG?

java.security.SecureRandom, among others, has two methods: generateSeed(int numBytes)and nextBytes(byte[] bytes). The former receives entropy from an external source and is less predictable, but slower; the latter uses the PRNG sequence and is more predictable, but much faster.

I want to have one java.security.SecureRandomto sow several PRNG MersenneTwisterFast, and my question is, is it safe enough for their seed to be sown nextByteswhile it SecureRandomwas sown safely in the first place?