# satisfiability – How to prove that \$overline{L}\$ is a strong connected component of an implication graph

Let $$G$$ be an implication graph.
Suppose that a set $$L$$ of literals is a strong connected component of $$G$$. Show that the set $$overline{L} = {overline{l}space vert space l in L}$$ is also a strong connected component of $$G$$. (Hint: Show by induction that for every path from $$l$$ to $$l′$$ a path from $$overline{l′}$$ to $$l$$ exists).
I know that $$overline{L}$$ must also be a strong connected component of $$G$$, but how can I prove it using induction? Or is there another way to prove it?