Well, one thing you can do is to assume the negation of what you want to prove, and then deduce a contradiction from that assumption. You can then argue that since the negation of the assumption you assume cannot be true (since it implies a contradiction) then what you wanted to prove is true.
1. you assume the negation of what you want to prove.
2. you deduce a contradiction from that assumption.
3. You concluded that what you want to prove is true.
This is an RAA proof. (Look up "conditional proof" in Google. Or "indirect proof") RAA is one kind of indirect proof.
Careful. It is often the case that it is not the assumption by itself that implies a contradiction and it is not that, therefore, that is impossible ("cannot be true") it is the conjunction of the propositions (assumption and others) that implies a contradiction
. The difference is that instead of it following that "the assumption cannot be true" it merely follow that "the assumption is not true". You got this right, of course, but your language use is dangerous. I've seen too many RAA arguments conclude that something is impossible (and they don't rely on all necessarily true premises).