# What contradiction are we looking for when using proof by contradiction?

If we want to prove a statement, “if $$p$$, then $$q$$“, by using the technique of proof by contradiction, we would suppose that “$$p$$ and ~$$q$$ are true” then we derive a contradiction.
Assume that ~$$q$$ implies $$w$$ is true. If we can argue that $$w$$ is not true by analyzing $$p$$, can we say that we have proved the “if, then” statement by contradiction?