Comment by laichzeit0

What’s assumed and not explicitly stated is the law of the excluded middle. That A is true or A is false and those are the only 2 possibilities. If you assume the law of the excluded middle then it’s impossible that “A or not-A” is false. So it’s true. But “A or not-A” is true is equivalent to “A and not-A” is false (just apply DeMorgan). So proof by contradiction is you assuming something B is true and it leading to a “A and not-A” (contradiction) so clearly B must be false.