I'm taking a class on Markov Processes and my professor claimed that we can sum up $P(A|X_{1}=x_{1},X_{2}=x_{2})$ over all possible $x_{2}$ and thus eliminate term $X_{2}$. I assume he meant that $$ \sum_{x_{2} \in I}\mathbb{P}(A|X_{1}=x_{1},X_{2}=x_{2}) = P(A|X_{1} = x_{1}) $$ where $I$ is a countable state space. What he claimed doesn't seem to be true in my opinion, so any ideas on what he could possibly mean?
P.S. I'm sorry that I forgot when this occurred exactly, but I will edit the post if I find out. I did look through posts but did not really find anything that directly answers my question