Suppose R is a commutative ring with 1, I $\subset R$ is an ideal.
We have R-Modules A, B and C with C being flat, as well as a short exact sequence
$0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$
Consider the induced sequence
$0 \rightarrow A/IA \rightarrow B/IB\rightarrow C/IC\rightarrow 0$
How do I prove that this sequence is exact? I have no idea how the flatness of C could come into play, or to be more specific, how I can use the exactness of $C\otimes\_$ (this is the only definition of flatness we have so far).
Any advice in the right direction would be appreciated.