I am currently reading a book which begins its portfolio theory section with the case with $n$ risky assets where it proves that 2-fund separation applies (any minimum variance portfolio is a linear combination of two minimum variance portfolios with distinct returns). It then moves on to the case where there's a riskfree asset as well, and claims at one point that each agent will hold a mix of the tangent portfolio and the riskfree asset.
Why? A result like this would require reproving 2-fund-separation in this new situation as well, but the author doesn't mention it at all. Is there then a different way to see this result, or is it just 2fundseparation that the author just forgot to mention still holds?