The idea for the security notion of Cryptographically Secure Random Number Generators (CSPRNGs) is that at the very least they are as good as Pseudo-Random Generators (PRG) which is why I'm applying their security notion of Indistinguishability.
This says that the probability that somebody can distinguish a PRG from a truly random sequence is better than guessing is negligible.
Now what you want to is to truncate the output of a CSPRNG (that is, you straight-up discard certain bits from the output). Now assume the result was insecure. As this truncated part would also be output by the actual CSPRNG, you could then "just" use this sub-part of the output and use the weakness we assumed to distinguish the CSPRNG's output from random. Now we assumed this to be impossible, so it can't be that such a weakness as assumed above exists and thus it must be secure.
A similar argument applies if you apply a public bijection on the output or a part of it.